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A176470

Primes of the form 5*x^2 - 3*y^2, where x and y are consecutive numbers.

5, 17, 53, 137, 173, 257, 677, 1097, 1193, 1733, 2237, 2657, 2957, 4133, 5297, 5717, 8573, 8837, 9377, 11093, 11393, 12953, 14957, 17477, 18233, 18617, 19793, 23537, 24413, 29033, 30497, 33533, 36713, 40037, 41177, 45293, 48353

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OFFSET

1,1

COMMENTS

a(n) is congruent to 1 (mod 4).

Primes of the form 2*k^2 + 10*k + 5 or 2*k^2 - 6*k - 3. - Vincenzo Librandi, Apr 19 2010

LINKS

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

MATHEMATICA

Select[Table[5n^2-3(n+1)^2, {n, 4, 200}], PrimeQ] (* Harvey P. Dale, Aug 07 2017 *)

PROG

(Magma) [ p: p in PrimesUpTo(60000) | exists(t){ n: n in [1..Isqrt(p)] | p eq 5*n^2-3*(n-1)^2 } ]; //y = x-1

CROSSREFS

Sequence in context: A191139 A107167 A201478 * A240693 A278464 A349974

Adjacent sequences: A176467 A176468 A176469 * A176471 A176472 A176473

KEYWORD

nonn

AUTHOR

Giovanni Teofilatto, Apr 18 2010

EXTENSIONS

Comment corrected by Giovanni Teofilatto, Apr 19 2010

STATUS

approved

URL: https://oeis.org/A176470

⇱ A176470 - OEIS