A382264 Semiprimes that are the sum of the m-th prime and the m-th semiprime for some m.
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
Keywords
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.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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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]);
Comments