cp's OEIS Frontend

A234739 Largest prime divisor of all composite numbers of the form k^2+1 between two consecutive primes of the same form.

%I A234739 #18 May 07 2025 17:15:12
%S A234739 5,13,41,61,113,181,97,313,613,761,1301,89,2113,2521,3121,3613,1693,
%T A234739 5101,1277,557,7321,601,1613,8581,10513,2161,4621,12641,14281,15313,
%U A234739 6337,16381,20201,21013,21841,24421,5153,26681,11329,30013,977,13313,34061,7129
%N A234739 Largest prime divisor of all composite numbers of the form k^2+1 between two consecutive primes of the same form.
%C A234739 Or, largest of all prime factors of composite numbers in A002522 between two consecutive primes A002496(n) and A002496(n+1).
%e A234739 181 is in the sequence because the composites between the two primes A002496(7)= 16^2+1 = 257 and A002496(8)= 20^2+1=401 are: 17^2+1= 2*5*29; 18^2+1 = 5*5*13; 19^2+1=2*181 and the largest prime divisor is 181, so a(5)=181.
%p A234739 with(numtheory):T:=array(1..111):k:=0:for n from 2 by 2 to 1000 do: p:=n^2+1:if type(p,prime)=true then k:=k+1:T[k]:=p:else fi:od:for i from 1 to k do:d0:=0:a:=sqrt(T[i]-1):b:=sqrt(T[i+1]-1):for j from a+1 to b-1 do:y:=factorset(j^2+1):n1:=nops(y):d:=y[n1]:if d>d0 then d0:=d:else fi:od: printf(`%d, `,d0):od:
%Y A234739 Cf. A002522, A002496, A238138, A238139.
%K A234739 nonn
%O A234739 1,1
%A A234739 _Michel Lagneau_, Dec 30 2013