cp's OEIS Frontend

A378945 Record values in A378898.

%I A378945 #12 Dec 12 2024 09:27:30
%S A378945 1,5,7,13,25,27,29,31,35,41,47,53,65,73,77,103,113,119,149,179,181,
%T A378945 215,233,235,251,319,413,425,433,455,473,485,491,529,535,557,659,725
%N A378945 Record values in A378898.
%C A378945 Numbers m > 0 such that for some k, (m+k)^2 + k^2 is prime while (m'+k)^2 + k^2 is not prime for 0 < m' < m, and for every k' < k there is m' < m such that (m'+k')^2 + k'^2 is prime.
%C A378945 The values of k are in A378946.
%F A378945 a(n) = A378898(A378946(n)).
%e A378945 a(1) = 1 = A378898(1), as (1+1)^2 + 1^2 = 5 is prime.
%e A378945 a(2) = 5 = A378898(3), as (5+3)^2 + 3^2 = 73 is prime, is the first value of A378898 greater than 1.
%e A378945 a(3) = 7 = A378898(13), as (7+13)^2 + 13^2 = 569 is prime, is the first value of A378898 greater than 5.
%p A378945 f:= proc(k) local m;
%p A378945   for m from 1 by 2 do
%p A378945     if igcd(m,k) = 1 and isprime((k+m)^2 + k^2) then return m fi
%p A378945   od
%p A378945 end proc:
%p A378945 R:= NULL: count:= 0: rec:= 0:
%p A378945 for k from 1 while count < 30 do
%p A378945   v:= f(k);
%p A378945   if v > rec then
%p A378945     count:= count+1;
%p A378945     R:= R, v;
%p A378945     rec:= v;
%p A378945   fi
%p A378945 od:
%p A378945 R;
%Y A378945 Cf. A378898, A378946.
%K A378945 nonn,more
%O A378945 1,2
%A A378945 _Robert Israel_, Dec 11 2024