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A370162
Semiprimes that are the sum of two successive semiprimes and also the sum of three successive semiprimes.
3
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
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
KEYWORD
nonn
AUTHOR
Zak Seidov and Robert Israel, Feb 26 2024
STATUS
approved