A129904 - OEIS

%I #19 Oct 18 2020 15:52:29

%S 7,13,19,31,37,43,49,61,67,73,79,91,97,103,109,127,133,139,151,157,

%T 163,169,181,193,199,211,217,223,229,241,247,259,271,277,283,301,307,

%U 313,331,337,343,349,361,367,373,379,397,403,409,421,427,433,439,457,463

%N 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 Is this A004611 without the 1? - _R. J. Mathar_, Jul 16 2020

%C a(n) = A004611(n+1) for (at least) n <= 10^6. - _Hugo Pfoertner_, Oct 17 2020

%e 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 isA129904 := proc(k)

%p     local i,j ;

%p     if modp(k,6) = 1 and k> 1 then

%p         for i from 0 to k-1 do

%p             j := k-1-i ;

%p             if modp(A003215(i),k) =0 and modp(A003215(j),k) =0 then

%p                 return true;

%p             end if;

%p         end do:

%p         false ;

%p     else

%p         false;

%p     end if;

%p end proc:

%p for k from 1 to 400 do

%p     if isA129904(k) then

%p         printf("%d,",k) ;

%p     end if;

%p end do:

%o (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 for(k=1,500,if(isA129904(k),print1(k,", "))) \\ _Hugo Pfoertner_, Oct 17 2020

%Y Cf. A003215, A016921, A004611.

%K nonn

%O 1,1

%A _Mats Granvik_, Jun 04 2007

%E Extended by _R. J. Mathar_, Dec 16 2016