A382186 Prime numbers that are the sum of the m-th prime and the m-th semiprime for some m.

17, 41, 71, 131, 281, 331, 353, 397, 449, 487, 563, 953, 1279, 1289, 1409, 1627, 2621, 2999, 3533, 3631, 3697, 3989, 4057, 4133, 4523, 4603, 4733, 4919, 5273, 5591, 5641, 6211, 6247, 6269, 6299, 6469, 6803, 7753, 7879, 7937, 8353, 8543, 8971, 8999, 9041, 9181, 9413, 9479, 9787, 9887, 9941, 10487

Offset

1,1

Comments

Primes in A133796.

Corresponding m's are in A092108.

Links

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

Formula

a(n) = A133796(A092108(n)).

Example

a(3) = 71 is a term because 71 = 37 + 34 is prime, where 37 is the 12th prime and 34 is the 12th semiprime.

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(isprime, P[1..m] + S[1..m]);

Mathematica

sp=Select[Range[3300], PrimeOmega[#]==2&]; p=Prime[Range[Length[sp]]]; Select[p+sp, PrimeQ] (* James C. McMahon, Mar 20 2025 *)

Crossrefs

Cf. A000040, A001358, A092108, A133796.

Sequence in context: A237659 A350052 A078655 * A052279 A147215 A126790

Adjacent sequences: A382183 A382184 A382185 * A382187 A382188 A382189

Keyword

nonn

Author

Zak Seidov and Robert Israel, Mar 18 2025

Status

approved