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 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. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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 A066938 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

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Last modified May 29 05:41 EDT 2022. Contains 354122 sequences. (Running on oeis4.)