A370162 Semiprimes that are the sum of two successive semiprimes and also the sum of three successive semiprimes.

134, 597, 614, 898, 982, 998, 1649, 2045, 2078, 2126, 2386, 2705, 2855, 2935, 3394, 3418, 3899, 5533, 5686, 5959, 6982, 7721, 8567, 8986, 9182, 9722, 9998, 10342, 10587, 10862, 10942, 11015, 11363, 11602, 11667, 11962, 13238, 13606, 14054, 14138, 14506, 14614, 15658, 15802, 15898, 16138, 16382

Offset

1,1

Links

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

Example

a(3) = 614 is a term because 614 = 2 * 307 is a semiprime, A001358(98) = 305 = 5 * 61 and A001358(99) = 309 = 3 * 103 are two successive semiprimes whose sum is 614, and A001358(65) = 203 = 7 * 29, A001358(66) = 205 = 5 * 41 and A001358(67) = 206 = 2 * 103 are three successive semiprimes whose sum is 614.

Maple

N:= 10^5: # for terms <= N
P:= select(isprime, [2, seq(i, i=3..N/2, 2)]):
nP:= nops(P):
SP:= 0:
for i from 1 while P[i]^2 <= N do
  m:= ListTools:-BinaryPlace(P, N/P[i]);
  SP:= SP, op(P[i]*P[i..m]);
od:
SP:= sort([SP]):
SS:= ListTools:-PartialSums(SP):
SS2:= {seq(SS[i]-SS[i-2], i=3..nops(SS))}:
SS3:= {seq(SS[i]-SS[i-3], i=4..nops(SS))}:
A:=SS2 intersect SS3 intersect convert(SP, set):
sort(convert(A, list));

Crossrefs

Cf A001358, A118717. Intersection of A092192 and A131610.

Sequence in context: A051387 A177348 A275997 * A007251 A219443 A348815

Adjacent sequences: A370159 A370160 A370161 * A370163 A370164 A370165

Keyword

nonn

Author

Zak Seidov and Robert Israel, Feb 26 2024

Status

approved