Search: a079781 -id:a079781
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2, 5, 11, 11, 59, 59, 419, 839, 2519, 2519, 27719, 27719, 360359, 360359, 360359, 720719, 12252239, 12252239, 232792559, 232792559, 232792559, 232792559, 5354228879, 5354228879, 26771144399, 26771144399, 80313433199, 80313433199, 2329089562799, 2329089562799
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OFFSET
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1,1
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COMMENTS
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For n >= 4, a(n) = A003418(n) - 1. Also for n < 4, a(n) is the smallest number congruent to (i-1) (mod i) for any i in {1..n}. That results directly from the definition of A003418 (if p == 0 (mod q), p-1 == (q-1) (mod q)) and from the first comment. - Philippe LALLOUET (philip.lallouet(AT)wanadoo.fr), Aug 29 2007
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LINKS
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EXAMPLE
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a(4) = lcm(1, 2, 3, 4) - 1 = 12 - 1 = 11. a(5) = lcm(1, 2, 3, 4, 5) - 1 = 60 - 1 = 59. - Michael Somos, Feb 28 2014
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MAPLE
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A079782 := proc(n) local a, found, r ; a := n+1 ; while true do found := true ; for r from 1 to n do if (a+r-1) mod (n-r+1) <> 0 then found := false ; break ; fi ; od ; if found then RETURN(a+n-1) ; fi ; a :=a+1 ; od ; end: for n from 1 to 20 do print(A079782(n)) ; od ; # R. J. Mathar, Nov 12 2006
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MATHEMATICA
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a[n_] := Which[n == 1, 2, n == 2, 5, n == 3, 11, True, LCM@@ Range[n] - 1];
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PROG
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(PARI) okrow(m, n) = {v = vector(n, i, i+m-1); for (i=1, n, if (v[i] % (n-i+1), return (0)); ); return (1); }
a(n) = {m = n+1; while (! okrow(m, n), m++); m+n-1; } \\ Michel Marcus, Feb 28 2014
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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2, 9, 30, 38, 285, 339, 2912, 6684, 22635, 25145, 304854, 332562, 4684589, 5044935, 5405280, 11531384, 208287927, 220540149, 4423058450, 4655850990, 4888643529, 5121436067, 123147263964, 128501492820, 669278609675, 696049754049, 2168462696022, 2248776129194
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OFFSET
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1,1
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LINKS
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FORMULA
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EXAMPLE
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The fifth row 55,56,57,58,59 is divisible by 5,4,3,2 and 1 respectively.
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MATHEMATICA
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a[n_] := n*(Which[n == 1, 2, n == 2, 5, n == 3, 11, True, LCM @@ Range[n] - 1] - (n-1)/2);
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PROG
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(PARI) okrow(m, n) = {v = vector(n, i, i+m-1); for (i=1, n, if (v[i] % (n-i+1), return (0)); ); return (1); }
a(n) = {m = n+1; while (! okrow(m, n), m++); sum(k=1, n, m+k-1); } \\ Michel Marcus, Feb 28 2014
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A079784
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Triangle read by rows in which the n-th row contains the smallest set of n consecutive numbers such that the r-th number in the n-th row is divisible by n-r+1. The first term of the n-th row must exceed n.
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+10
3
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2, 4, 5, 9, 10, 11, 8, 9, 10, 11, 55, 56, 57, 58, 59, 54, 55, 56, 57, 58, 59, 413, 414, 415, 416, 417, 418, 419, 832, 833, 834, 835, 836, 837, 838, 839, 2511, 2512, 2513, 2514, 2515, 2516, 2517, 2518, 2519, 2510, 2511, 2512, 2513, 2514, 2515, 2516, 2517, 2518, 2519
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OFFSET
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1,1
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LINKS
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EXAMPLE
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Triangle starts:
2;
4, 5;
9, 10, 11;
8, 9, 10, 11;
55, 56, 57, 58, 59;
54, 55, 56, 57, 58, 59;
413, 414, 415, 416, 417, 418, 419;
...
The fifth row 55,56,57,58,59 is divisible by 5,4,3,2 and 1 respectively.
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MATHEMATICA
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T[n_, k_] := T[n, k] = Which[n == k == 1, 2, n == k == 2, 5, n == k == 3, 11, n == k, LCM @@ Range[n] - 1, True, T[n, k + 1] - 1];
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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Corrected and extended by Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 29 2003
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STATUS
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approved
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