A261465 a(n) = prime(n+1)^2 - prime(n).

7, 22, 44, 114, 158, 276, 344, 510, 818, 932, 1338, 1644, 1808, 2166, 2762, 3428, 3662, 4428, 4974, 5258, 6168, 6810, 7838, 9320, 10104, 10508, 11346, 11774, 12660, 16016, 17034, 18638, 19184, 22062, 22652, 24498, 26412, 27726, 29762

Offset: 1

Author

Altug Alkan, Aug 20 2015

Keywords

• nonn
• easy

Examples

			a(2) = 5^2 - 3 = 22.
		

Crossrefs

Cf. A036689, A001223, A069482, A129701.

Programs

Magma

[NthPrime(n+1)^2-NthPrime(n): n in [1.. 70]]; // Vincenzo Librandi, Aug 20 2015

Mathematica

Table[Prime[n + 1]^2 - Prime[n], {n, 60}] (* Vincenzo Librandi, Aug 20 2015 *)

PARI

first(m)=vector(m,i,prime(i+1)^2 - prime(i)) \\ Anders Hellström, Aug 20 2015

PARI

a(n,p=prime(n)); nextprime(p+1)^2-p \\ Charles R Greathouse IV, Aug 22 2015

PARI

first(n)=my(v=primes(n+1)); vector(n,i,v[i+1]^2-v[i]) \\ Charles R Greathouse IV, Aug 22 2015

Formula

a(n) = A036689(n+1) + A001223(n). - Michel Marcus, Aug 21 2015 [Corrected by Georg Fischer, Dec 12 2022]

a(n) ~ n^2 log^2 n. - Charles R Greathouse IV, Aug 22 2015