# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a249077 Showing 1-1 of 1 %I A249077 #34 Sep 08 2022 08:46:10 %S A249077 3,5,7,11,13,19,31,41,61,67,73,79,83,89,97,103,137,139,149,151,157, %T A249077 181,193,199,211,223,227,239,241,271,311,317,331,337,349,373,421,433, %U A249077 439,443,449,461,607,619,631,643,661,691,719,739,757,811,823,829,853,859 %N A249077 Primes of the form n^2 + k such that n^2 - k is also prime, where -n < k < n. %C A249077 Members of a pair (a, b) of primes such that a < b and the distances from a and b to the nearest square above a (or below b) are equal. %C A249077 The only prime of the form n^2 + 1 (A002496) in the sequence is 5. %C A249077 Is this sequence infinite? %F A249077 A prime p is in the sequence if and only if 2*A053187(p)-p is prime. %e A249077 2^2-1=3, 2^2+1=5, both prime. %e A249077 8^2-3=61, 8^2+3=67, both prime. %p A249077 g:= proc(t,m) if isprime(m+t) and isprime(m-t) then (m+t,m-t) else NULL fi end proc: %p A249077 `union`(seq(map(g,{$1..n-1},n^2),n=2..100)); %p A249077 # if using Maple 11 or earlier, uncomment the next line %p A249077 # sort(convert(%,list)); %p A249077 # _Robert Israel_, Oct 31 2014 %o A249077 (Magma) lst:=[]; for m in [1..28] do r:=m*(m+1)+1; s:=(m+1)^2; for a in [r..s-1] do if IsPrime(a) then b:=2*s-a; if IsPrime(b) then Append(~lst, a); Append(~lst, b); end if; end if; end for; end for; Sort(lst); %o A249077 (PARI) for(n=1, 859, if(issquare(n), x=ps=n; until(issquare(x), x++); ns=x); if(isprime(n), if(n-ps