A254712 -id:A254712 - cp's OEIS frontend

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

Zak Seidov, Dec 29 2015

nonn

			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.

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

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

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

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

A265438 Smallest semiprime that is the sum of n consecutive semiprimes.

Original entry on oeis.org

4, 10, 25, 39, 69, 58, 133, 122, 249, 209, 185, 219, 254, 327, 458, 377, 473, 579, 745, 589, 951, 898, 1047, 843, 917, 1382, 1157, 1243, 1247, 1678, 1514, 1895, 1703, 1707, 2138, 2147, 2599, 2157, 2509, 2515, 2519, 2642, 2771, 3566, 4126, 3317, 3599, 3891, 4198, 3755, 4369, 4223, 4227

Offset: 1

Zak Seidov, Dec 09 2015

nonn

The sequence is non-monotonic. But are all the terms distinct?

A092190 is a subsequence. More precisely, a(A092189(k)) = A092190(k). - Altug Alkan, Dec 13 2015

			a(1) = 4 = A001358(1),
a(2) = 10 = A001358(3) = A092192(1) = A001358(1)+A001358(2) = 4+6,
a(3) = 25 = A001358(9) = A131610(1),
a(4) = 39 = A001358(15) = A158339(1),
a(5) = 69 = A001358(24) = A254712(1),
a(6) = 58 = A001358(21) = A266451(1).

Zak Seidov, Table of n, a(n) for n = 1..1000

Cf. A001358, A092190, A092192, A131610, A158339, A254712.

cp's OEIS Frontend

A266451 Semiprimes that are the sum of six consecutive semiprimes.

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