A370685 Semiprimes that are also the sums of two, three and four successive semiprimes.

2045, 2705, 2855, 14614, 18838, 28437, 31299, 43603, 68807, 76841, 77386, 88041, 108415, 116822, 194605, 213679, 218729, 252094, 255202, 269653, 290449, 294683, 302761, 305362, 310799, 339382, 348242, 361055, 398111, 445066, 445174, 459761, 464567, 489809, 496081, 501386, 515981, 534777, 544405

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..2734

Example

a(3) = 2855 is a term because 2855 = 5 * 571 is a semiprime, A001358(423) = 1418 = 2*709 and A001358(424) = 1437 = 3 * 479 are two successive semiprimes whose sum is 2855, A001358(285) = 949 = 13 * 73, A001358(286) = 951 = 3 * 317 and A001358(287) = 955 = 5 * 191 are three successive semiprimes whose sum is 2855, and A001358(216) = 707 = 7 * 101, A001358(217) = 713 = 23 * 31, A001358(218) = 717 = 3 * 239, A001358(219) = 718 = 2 * 359 are four successive semiprimes whose sum is 2855.

Maple

N:= 10^6: # 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))}:
SS4:= {seq(SS[i]-SS[i-4], i=5..nops(SS))}:
A:=SS2 intersect SS3 intersect SS4 intersect convert(SP, set):
A:= sort(convert(A, list)):

Crossrefs

Cf. A001358, A370162. Intersection of A092192, A131610 and A158339.

Sequence in context: A115553 A068264 A024021 * A298756 A145590 A241039

Adjacent sequences: A370682 A370683 A370684 * A370686 A370687 A370688

Keyword

nonn

Author

Robert Israel, Feb 26 2024

Status

approved