A349660 Numbers which are the sum of a prime and the square of the next prime.

11, 28, 54, 128, 180, 302, 378, 548, 864, 990, 1400, 1718, 1890, 2252, 2856, 3534, 3780, 4550, 5108, 5400, 6314, 6968, 8004, 9498, 10298, 10710, 11552, 11988, 12878, 16242, 17288, 18900, 19458, 22340, 22950, 24800, 26726, 28052, 30096, 32214, 32940, 36662

Offset: 1

Author

Karl-Heinz Hofmann, Nov 24 2021

Keywords

• nonn
• easy

Examples

			a(2) = 3 + 5^2 = 28; a(3) = 5 + 7^2 = 54.
		

Links

• Karl-Heinz Hofmann, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A140511, A000040, A001248, A036690, A001223, A001043, A036689, A349661, A124129.

Programs

Mathematica

nterms=100;Table[Prime[n]+Prime[n+1]^2,{n,nterms}] (* Paolo Xausa, Nov 24 2021 *)

PARI

a(n) = prime(n) + prime(n+1)^2; \\ Michel Marcus, Nov 24 2021

Python

from sympy import sieve;
for n in range(1,10001): print(sieve[n] + sieve[n+1]**2)

Formula

a(n) = prime(n) + prime(n+1)^2.

a(n) = A000040(n) + A001248(n+1).

a(n) = A036690(n+1) - A001223(n).

a(n) = A001043(n) + A036689(n+1). - Michel Marcus, Nov 24 2021