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A124434
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LCM (least common multiple) of A001043 (sum of consecutive primes) and A001223 (difference of consecutive primes).
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3
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5, 8, 12, 36, 24, 60, 36, 84, 156, 60, 204, 156, 84, 180, 300, 336, 120, 384, 276, 144, 456, 324, 516, 744, 396, 204, 420, 216, 444, 1680, 516, 804, 276, 1440, 300, 924, 960, 660, 1020, 1056, 360, 1860, 384, 780, 396, 2460, 2604, 900, 456, 924, 1416, 480, 2460
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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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a(n) = lcm((prime(n+1)+prime(n)), (prime(n+1)-prime(n))).
a(n) = (prime(n+1)^2 - prime(n)^2)/2 for n > 1. - Jon Maiga, Jan 17 2019
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EXAMPLE
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a(3)=12 because prime(3)=5, prime(4)=7 and lcm(7+5, 7-5) = lcm(12,2) = 12.
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MATHEMATICA
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LCM[Total[#], #[[2]]-#[[1]]]&/@Partition[Prime[Range[60]], 2, 1] (* Harvey P. Dale, Apr 19 2013 *)
Join[{5}, Table[(Prime[n + 1]^2 - Prime[n]^2)/2, {n, 2, 59}]] (* Jon Maiga, Jan 17 2019 *)
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PROG
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(PARI) a(n) = my(p = prime(n), q = prime(n+1)); lcm(q+p, q-p); \\ Michel Marcus, Mar 15 2018
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CROSSREFS
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KEYWORD
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AUTHOR
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Mitch Cervinka (Mitch.Cervinka(AT)eds.com), Dec 15 2006
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STATUS
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approved
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