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

Author

Zak Seidov and Robert Israel, Feb 26 2024

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf A001358, A118717. Intersection of A092192 and A131610.

Programs

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));