cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A382264 Semiprimes that are the sum of the m-th prime and the m-th semiprime for some m.

Original entry on oeis.org

6, 9, 14, 25, 38, 55, 86, 122, 141, 158, 178, 185, 218, 262, 301, 326, 446, 466, 537, 634, 695, 723, 758, 785, 866, 878, 886, 895, 898, 921, 993, 1006, 1041, 1047, 1077, 1099, 1126, 1138, 1154, 1198, 1214, 1219, 1234, 1262, 1366, 1466, 1535, 1679, 1706, 1751, 1774, 1779, 1822, 1977, 2026, 2173
Offset: 1

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Author

Zak Seidov and Robert Israel, Mar 19 2025

Keywords

Comments

Semiprimes in A133796.
Corresponding m's are A092021.

Examples

			a(4) = 25 is a term, because 25 = 5^2 is a semiprime and 25 = 11 + 14 where 11 is the 5th prime and 14 is the 5th semiprime.
		

Crossrefs

Programs

  • Maple
    N:= 10000: # for terms where the m-th prime and m-th semiprime are <= N
    P:= select(isprime, [2, seq(i, i=3..N, 2)]): nP:= nops(P):
    S:= NULL:
    for i from 1 to nP while P[i]^2 <= N do
      jmax:= ListTools:-BinaryPlace(P, N/P[i]);
      S:= S, op(P[i..jmax] *~ P[i]);
    od:
    S:= sort([S]):
    m:= min(nP, nops(S)):
    select(t -> numtheory:-bigomega(t)=2, P[1..m] + S[1..m]);

Formula

a(n) = A133796(A092021(n)).
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