A264778 - OEIS

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A264778

Numbers k such that 6*k+1, 3*k+2, 6*k+7 are all odd semiprimes.

113, 157, 193, 209, 211, 223, 231, 235, 251, 259, 307, 319, 345, 401, 415, 437, 463, 489, 521, 563, 567, 581, 599, 663, 673, 677, 701, 719, 731, 733, 771, 789, 811, 855, 857, 875, 883, 923, 935, 951, 961, 983, 993, 995, 997, 1017, 1023, 1031, 1047, 1089, 1097

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OFFSET

1,1

COMMENTS

Or odd numbers k such that the arithmetic progression 6*k+1, 6*k+4, 6*k+7 consists of twice a semiprime sandwiched between two semiprimes.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

MATHEMATICA

fQ[n_] := And[OddQ@ n, PrimeOmega@ n == 2]; Select[Range@ 1100,

AllTrue[{6 # + 1, 3 # + 2, 6 # + 7}, fQ] &] (* Michael De Vlieger, Nov 24 2015, Version 10 *)

PROG

(PARI) for(n=1, 1e4, if(n%2==1 && bigomega(6*n+1)==2 && bigomega(3*n+2)==2 && bigomega(6*n+7)==2, print1(n, ", "))); \\ Altug Alkan, Nov 24 2015