A266451 Semiprimes that are the sum of six consecutive semiprimes.

58, 91, 123, 142, 161, 205, 278, 473, 566, 614, 706, 718, 802, 838, 851, 889, 1079, 1211, 1226, 1238, 1262, 1286, 1385, 1415, 1633, 1714, 1819, 1891, 1945, 2005, 2123, 2147, 2194, 2217, 2327, 2374, 2427, 2563, 2594, 2653, 2771, 2815, 2854, 2947, 2987, 3118, 3133, 3151, 3199, 3214, 3305, 3379

Offset: 1

Author

Zak Seidov, Dec 29 2015

Keywords

• nonn

Examples

			58 = A001358(21) = A001358(1) + ... + A001358(6) = 4+6+9+10+14+15,
91 = A001358(31) = A001358(3) + ... + A001358(8) = 9+10+14+15+21+22.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001358, A092192, A131610, A158339, A254712.

Programs

Maple

N:= 10^4: # to get all terms where the 6 consecutive semiprimes <= N
P:= select(isprime, [2,seq(i,i=3..N/2,2)]): nP:= nops(P):
SP:= NULL:
for i from 1 to nP do
  for j from 1 to nP while P[i]*P[j] <= N do od:
  SP:= SP, op(map(`*`,P[i],P[1..j-1]));
od:
SP:= sort(convert({SP},list)): nSP:= nops(SP):
select(numtheory:-bigomega=2, [seq(convert(SP[i..i+5],`+`),i=1..nSP-5)]): # Robert Israel, Nov 19 2017

Mathematica

Select[(Total[#] & /@ Partition[Select[Range[4, 9999], 2 == PrimeOmega[#] &], 6, 1]), 2 == PrimeOmega[#] &]