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A378946 Locations of records in A378898.

%I A378946 #8 Dec 12 2024 09:28:03
%S A378946 1,3,13,31,49,68,216,227,288,339,408,421,797,1176,1494,1947,3876,6453,
%T A378946 12108,12558,13272,24027,80667,92472,98154,186543,765351,2294838,
%U A378946 6815886,11105034,12608001,13669797,25343472,25485726,40937853,48562668,72974013,122175969
%N A378946 Locations of records in A378898.
%C A378946 The record values are in A378945.
%C A378946 Numbers k such that for some m, (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.
%F A378946 A378898(a(n)) = A378945(n).
%e A378946 a(1) = 1, as A378898(1) = 1, with (1+1)^2 + 1^2 = 5 prime.
%e A378946 a(2) = 3, as A378898(3) = 5, with (5+3)^2 + 3^2 = 73 prime, and 3 is the first k with  A378898(k) > 1.
%e A378946 a(3) = 13, as A378898(13) = 7, with (7+13)^2 + 13^2 = 569 prime, and 13 is the first k with A378898(k) > 5.
%p A378946 f:= proc(k) local m;
%p A378946   for m from 1 by 2 do
%p A378946     if igcd(m,k) = 1 and isprime((k+m)^2 + k^2) then return m fi
%p A378946   od
%p A378946 end proc:
%p A378946 J:= NULL: count:= 0: rec:= 0:
%p A378946 for k from 1 while count < 30 do
%p A378946   v:= f(k);
%p A378946   if v > rec then
%p A378946     count:= count+1;
%p A378946     J:= J, k;
%p A378946     rec:= v;
%p A378946   fi
%p A378946 od:
%p A378946 J;
%Y A378946 Cf. A378898, A378945.
%K A378946 nonn
%O A378946 1,2
%A A378946 _Robert Israel_, Dec 11 2024