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A217717 Primes of the form x^2 + y^2 - 1, where x and y are primes. 1
7, 17, 73, 97, 193, 241, 313, 337, 409, 457, 577, 1009, 1129, 1201, 1249, 1321, 1489, 1657, 1801, 1873, 2017, 2137, 2377, 2521, 2689, 2833, 2857, 3049, 3169, 3217, 3361, 3529, 3697, 3769, 3889, 4057, 4177, 4441, 4513, 4561, 4657, 5209, 5449, 5569, 5689, 5857 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Unlike primes of the form x^2+y^2 (A045637) which can be redefined as x^2+4, and primes of the form x^2+y^2+1 (A182475) which can be redefined as primes of the form x^2+10, this sequence appears to have no one-variable analog. In the preceding, x and y are prime.

LINKS

Christian N. K. Anderson, Table of n, a(n) for n = 1..10000

EXAMPLE

457 is in the sequence because it is a prime number, and 457 = 13^2 + 17^2 - 1.

MATHEMATICA

mx = 25; Union[Select[Flatten[Table[Prime[a]^2 + Prime[b]^2 - 1, {a, mx}, {b, a, mx}]], # < Prime[mx]^2 && PrimeQ[#] &]] (* T. D. Noe, Mar 29 2013 *)

CROSSREFS

Cf. A045637 (primes of the form p^2+4, where p is prime).

Cf. A182475 (primes of the form p^2+10, where p is prime).

Sequence in context: A216073 A086870 A107693 * A122528 A123206 A035078

Adjacent sequences:  A217714 A217715 A217716 * A217718 A217719 A217720

KEYWORD

nonn

AUTHOR

Kevin L. Schwartz and Christian N. K. Anderson, Mar 21 2013

STATUS

approved

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Last modified June 22 21:29 EDT 2021. Contains 345393 sequences. (Running on oeis4.)