A110833 -id:A110833 - cp's OEIS frontend

A165944 Primes of the form p^2 +3p + 1, where p is also a prime.

11, 19, 41, 71, 419, 599, 929, 1481, 1979, 2351, 2969, 3659, 4691, 13109, 19181, 19739, 25121, 27059, 30449, 32579, 53129, 57839, 66821, 69959, 86729, 98909, 122849, 125669, 129959, 140249, 144779, 176819, 202949, 219491, 250499, 254519

Offset: 1

Claudio Meller, Oct 01 2009

Primes of the form p +(p+1)^2 = A000040(k) + A110833(k).

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

[a: p in PrimesInInterval(1, 1000) | IsPrime(a) where a is (p^2 + 3*p + 1)]; // Vincenzo Librandi, Jun 13 2014

Select[Table[p^2 + 3 p + 1, {p, Prime[Range[300]]}], PrimeQ] (* Vincenzo Librandi, Jun 13 2014 *)

Entries checked - R. J. Mathar, Oct 05 2009

A178398 a(n) = p(p+1)^2, where p is the n-th prime.

Original entry on oeis.org

18, 48, 180, 448, 1584, 2548, 5508, 7600, 13248, 26100, 31744, 53428, 72324, 83248, 108288, 154548, 212400, 234484, 309808, 368064, 399748, 505600, 585648, 720900, 931588, 1050804, 1114048, 1248048, 1318900, 1468548, 2080768, 2282544, 2609028, 2724400, 3352500, 3488704, 3919348, 4384048, 4713408, 5237748, 5799600, 5995444, 7041024, 7263748, 7723188, 7960000, 9483184, 11189248, 11800368, 12114100

Offset: 1

Eduard Mayer, Dec 21 2010

nonn

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Table[p (p+1)^2,{p,Prime[Range[50]]}] (* Harvey P. Dale, Aug 12 2025 *)

a(n) = prime(n)*(prime(n)+1)^2 \\ Michel Marcus, Jun 24 2013

a(n) = A000040(n)*A110833(n) = A000040(n)*A008864(n)^2 = A008864(n)*A036690(n). - Michel Marcus, Jun 24 2013

Sum 1/a(n) = A382567. - R. J. Mathar, Mar 31 2025

Edited by N. J. A. Sloane, Dec 21 2010

cp's OEIS Frontend

A165944 Primes of the form p^2 +3p + 1, where p is also a prime.

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