A337359 Primes r between two consecutive squares of primes p^2 and q^2 such that p^2 + q^2 - r is prime as well.

11, 17, 23, 31, 37, 43, 61, 67, 73, 97, 103, 109, 127, 139, 151, 163, 181, 229, 277, 313, 337, 367, 433, 457, 523, 541, 547, 601, 613, 619, 631, 643, 661, 709, 727, 739, 751, 757, 769, 823, 829, 883, 919, 1009, 1033, 1039, 1051, 1093, 1117, 1129, 1201, 1213, 1237, 1279

Offset

1,1

Comments

Certain terms are paired (e.g. 11 and 23, 31 and 43) but some terms are stand-alone (e.g. 17, 37) as they are the same distance from both consecutive prime squares. Unknown if this sequence terminates.

Links

David A. Corneth, Table of n, a(n) for n = 1..10000

Example

11 and 23 are terms because 11 = 3^2 + 2 = 5^2 - 14 and 23 = 3^2 + 14 = 5^2 - 2.
17 is a term because 17 = 3^2 + 8 = 5^2 - 8.

Prog

(PARI) ok(p)={if(p>4 && isprime(p), my(q=precprime(sqrtint(p))); isprime(nextprime(q+1)^2 + q^2 - p), 0)} \\ Andrew Howroyd, Aug 24 2020
(PARI) upto(n) = {q = 3; my(res = List()); forprime(p = 5, nextprime(sqrtint(n)), s = p^2 + q^2; forprime(r = q^2, s/2, if(isprime(s - r), listput(res, r); listput(res, s-r); ) ); q = p; ); Set(res); } \\ David A. Corneth, Aug 24 2020

Crossrefs

Sequence in context: A265402 A145481 A006621 * A275596 A158913 A363638

Adjacent sequences: A337356 A337357 A337358 * A337360 A337361 A337362

Keyword

nonn

Author

Isaac Walters, Aug 24 2020

Extensions

Terms a(42) and beyond from Andrew Howroyd, Aug 24 2020

Definition made precise by David A. Corneth, Aug 24 2020

a(32) corrected by David A. Corneth, Aug 25 2020

Status

approved