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A266451
Semiprimes that are the sum of six consecutive semiprimes.
2
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
1,1
LINKS
EXAMPLE
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.
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[#] &]
CROSSREFS
KEYWORD
nonn
AUTHOR
Zak Seidov, Dec 29 2015
STATUS
approved