cp's OEIS Frontend

A129904 Find the first two terms in A003215, say A003215(i) and A003215(j), that are divisible by a number in A016921 not 1, say by k = A016921(m). Then i + j + 1 = k and k is added to the sequence.

%I A129904 #19 Oct 18 2020 15:52:29
%S A129904 7,13,19,31,37,43,49,61,67,73,79,91,97,103,109,127,133,139,151,157,
%T A129904 163,169,181,193,199,211,217,223,229,241,247,259,271,277,283,301,307,
%U A129904 313,331,337,343,349,361,367,373,379,397,403,409,421,427,433,439,457,463
%N A129904 Find the first two terms in A003215, say A003215(i) and A003215(j), that are divisible by a number in A016921 not 1, say by k = A016921(m). Then i + j + 1 = k and k is added to the sequence.
%C A129904 Is this A004611 without the 1? - _R. J. Mathar_, Jul 16 2020
%C A129904 a(n) = A004611(n+1) for (at least) n <= 10^6. - _Hugo Pfoertner_, Oct 17 2020
%e A129904 A003215(1) = 7 is divisible by A016921(1) = 7, A003215(5) = 91 is divisible by A016921(1) = 7 and 5+1+1=7, so 7 is a member.
%p A129904 isA129904 := proc(k)
%p A129904     local i,j ;
%p A129904     if modp(k,6) = 1 and k> 1 then
%p A129904         for i from 0 to k-1 do
%p A129904             j := k-1-i ;
%p A129904             if modp(A003215(i),k) =0 and modp(A003215(j),k) =0 then
%p A129904                 return true;
%p A129904             end if;
%p A129904         end do:
%p A129904         false ;
%p A129904     else
%p A129904         false;
%p A129904     end if;
%p A129904 end proc:
%p A129904 for k from 1 to 400 do
%p A129904     if isA129904(k) then
%p A129904         printf("%d,",k) ;
%p A129904     end if;
%p A129904 end do:
%o A129904 (PARI) isA129904(k)={my(a003215(n)=3*n*(n+1)+1);if(k%6!=1||k<=1,0, for(i=0,k-1,my(j=k-1-i); if(a003215(i)%k==0&&a003215(j)%k==0, return(1))));0};
%o A129904 for(k=1,500,if(isA129904(k),print1(k,", "))) \\ _Hugo Pfoertner_, Oct 17 2020
%Y A129904 Cf. A003215, A016921, A004611.
%K A129904 nonn
%O A129904 1,1
%A A129904 _Mats Granvik_, Jun 04 2007
%E A129904 Extended by _R. J. Mathar_, Dec 16 2016