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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
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
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
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