A394471 Primes of the form prime(k) + prime(k+2) - 1, where prime(k) is the k-th prime.

19, 31, 47, 53, 71, 79, 113, 131, 139, 149, 167, 179, 199, 211, 263, 269, 313, 353, 373, 421, 467, 619, 643, 653, 677, 719, 829, 853, 887, 919, 941, 953, 1031, 1061, 1069, 1097, 1109, 1193, 1213, 1223, 1231, 1259, 1367, 1399, 1451, 1489, 1499, 1511, 1607, 1759

Offset

1,1

Links

Nikhil Sharma, Table of n, a(n) for n = 1..1000

Example

k=2: prime(2)+prime(4)-1 = 3+7-1 = 9 = 3*3, not prime, not a term.
k=3: prime(3)+prime(5)-1 = 5+11-1 = 15 = 3*5, not prime, not a term.
k=4: prime(4)+prime(6)-1 = 7+13-1 = 19, prime, so 19 is a term.
k=6: prime(6)+prime(8)-1 = 13+19-1 = 31, prime, so 31 is a term.

Maple

select(t -> isprime(prime(t)+prime(t+2)-1), [$2..100]);

Mathematica

Select[Table[Prime[k]+Prime[k+2]-1, {k, 2, 500}], PrimeQ]

Prog

(Python)
from sympy import prime, isprime
print([prime(k)+prime(k+2)-1 for k in range(2, 500) if isprime(prime(k)+prime(k+2)-1)])

Crossrefs

Cf. A111255, A023201, A001359, A005384, A005385.

Sequence in context: A096787 A104006 A117065 * A006035 A104485 A276569

Adjacent sequences: A394468 A394469 A394470 * A394472 A394473 A394474

Keyword

nonn

Author

Nikhil Sharma, Mar 21 2026

Status

approved