A175255 -id:A175255 - cp's OEIS frontend

A175256 a(n) = sqrt(A175255(n)).

2, 5, 13, 17, 19, 23, 31, 53, 71, 89, 113, 127, 157, 163, 167, 181, 197, 229, 347, 373, 401, 409, 419, 449, 487, 503, 509, 523, 541, 563, 571, 577, 599, 647, 751, 769, 773, 823, 827, 883, 919, 937, 941, 967, 971, 977, 1009, 1013, 1031, 1039, 1171, 1201, 1223

Offset: 1

Zak Seidov, Mar 15 2010

nonn

Zak Seidov, Table of n, a(n) for n=1..10000

Cf. A001248, A111153, A175255.

A362225 Primes of the form (2*p^2 + 1)/3 where p is a prime > 3.

Original entry on oeis.org

17, 113, 193, 241, 353, 641, 1873, 3361, 5281, 8513, 10753, 16433, 17713, 18593, 21841, 25873, 34961, 80273, 92753, 107201, 111521, 117041, 134401, 158113, 168673, 172721, 182353, 195121, 211313, 217361, 221953, 239201, 279073, 376001, 394241

Offset: 1

Alain Rocchelli, Apr 11 2023

nonn

The corresponding p values are the odd terms of A175256.

			17 is a term since for p=5, (2*p^2 + 1)/3 = (2*5^2 + 1)/3 = 17 and 17 is prime.

Cf. A175255, A175256.

Select[(2*Prime[Range[3, 140]]^2 + 1)/3, PrimeQ] (* Amiram Eldar, May 18 2023 *)

forprime(p=5, 1000, my(Ap=floor((2*p^2+1)/3)); if(isprime(Ap), print1(Ap,", ")))

a(n) = (2*A175255(n+1)+1)/3.

cp's OEIS Frontend

A175256 a(n) = sqrt(A175255(n)).

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A362225 Primes of the form (2*p^2 + 1)/3 where p is a prime > 3.

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