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

Author

Zak Seidov and Robert Israel, Mar 18 2025

Keywords

• nonn

Comments

Primes in A133796.

Corresponding m's are in A092108.

Examples

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

Links

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

Crossrefs

Cf. A000040, A001358, A092108, A133796.

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(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 *)

Formula

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