A342039 - OEIS

%I #10 Nov 14 2022 23:04:31

%S 256,27,10,42,40,66,40,72,66,42,390,333,180,301,46,104,145,1230,264,

%T 280,396,195,82,132,240,275,408,106,1566,364,693,2080,374,552,222,

%U 1725,2730,162,166,946,178,990,665,480,294,1386,4305,1221,226,456,348,952

%N a(n) is the index of the first occurrence of the term in A307437 that is divisible by p and greater than p, p = prime(n).

%C Different from A342038, here a nontrivial multiple of p is required.

%C a(n) exists for all n: from the formula in A307437 we know a((p-1)/2*p^e) = p^(e+1) if p is an odd prime and (p-1)*p^e+1 is composite. For fixed p, there exist infinitely many e such that (p-1)*p^e+1 is composite.

%C Conjecture: a(n) >= prime(n)-1 for all n.

%F For n = 3, prime(n) = 5. The first term in A307437 that is divisible by 5 and greater than 5 is A307437(10) = 25 = 5^2, hence a(3) = 10.

%F For n = 14, prime(n) = 47. The first term in A307437 that is divisible by 47 and greater than 47 is A307437(46) = 235 = 5*47, hence a(14) = 46.

%o (PARI) a(n) = my(p=prime(n)); for(k=1, oo, my(m=A307437(k)); if(m>p&&m%p==0, return(k))) \\ see A307437 for its program

%Y Cf. A307437, A342038.

%K nonn

%O 1,1

%A _Jianing Song_, Feb 26 2021