A201704 -id:A201704 - cp's OEIS frontend

A121068 Numbers k such that 8*k^2 + 7 is prime.

0, 3, 27, 30, 33, 48, 57, 60, 72, 75, 78, 108, 117, 123, 135, 150, 162, 192, 198, 207, 228, 243, 270, 300, 303, 312, 342, 345, 390, 408, 417, 423, 435, 480, 498, 507, 510, 513, 543, 552, 555, 573, 618, 633, 642, 645, 657, 675, 705, 723, 732, 738, 747, 750, 780

Offset: 1

Parthasarathy Nambi, Aug 10 2006

All terms are multiples of 3. - Zak Seidov, Aug 11 2006

A201704 is primes of form 8*k^2+7. James C. McMahon, Oct 12 2024

			If k=135 then 8*k^2 + 7 = 145807 (prime).

Cf. A007522, A201704.

[ n: n in [0..1500] | IsPrime(8*n^2 + 7) ]; // Vincenzo Librandi, Jan 31 2011

a:=proc(n) if isprime(8*n^2+7)=true then n else fi end: seq(a(n),n=0..1000); # Emeric Deutsch, Aug 11 2006

Select[Range[0,780],PrimeQ[8#^2+7]&] (* James C. McMahon, Oct 12 2024 *)

is(n)=isprime(8*n^2+7) \\ Charles R Greathouse IV, Jun 13 2017

More terms from Emeric Deutsch and Joshua Zucker, Aug 11 2006

A257163 Primes of the form 3n^2 + 2.

Original entry on oeis.org

2, 5, 29, 149, 509, 677, 1877, 3677, 8429, 9749, 11909, 13469, 17789, 22709, 27077, 28229, 45389, 46877, 53069, 70229, 72077, 81677, 100469, 102677, 114077, 128549, 141269, 154589, 180077, 192029, 195077, 207509, 223589, 230189, 261077, 312989, 340709, 352949, 395309, 399677, 426389

Offset: 1

Juri-Stepan Gerasimov, Apr 16 2015

Two together with A027864(n).

Generated by n = 0, 1, 3, 7, 13, 15, 25, 35, 53, 57, ...

			2 is in this sequence because 3*0^2 + 2 = 2 and 2 is prime.

Cf. A103564, A027864. Primes of the form k*n^2 + k - 1: A090698, this sequence, A121825, A201483, A201600, A201607, A201704.

[a: n in [0..400] | IsPrime(a) where a is (3*n^2+2)];

Select[Table[3 n^2 + 2, {n, 0, 400}], PrimeQ] (* Vincenzo Librandi, Apr 17 2015 *)

select(isprime, vector(100, n, 3*n^2-6*n+5)) \\ Charles R Greathouse IV, Apr 17 2015

cp's OEIS Frontend

A121068 Numbers k such that 8*k^2 + 7 is prime.

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