A342039 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).

256, 27, 10, 42, 40, 66, 40, 72, 66, 42, 390, 333, 180, 301, 46, 104, 145, 1230, 264, 280, 396, 195, 82, 132, 240, 275, 408, 106, 1566, 364, 693, 2080, 374, 552, 222, 1725, 2730, 162, 166, 946, 178, 990, 665, 480, 294, 1386, 4305, 1221, 226, 456, 348, 952

Offset

1,1

Comments

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

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.

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

Links

Table of n, a(n) for n=1..52.

Formula

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.

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.

Prog

(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

Crossrefs

Cf. A307437, A342038.

Sequence in context: A160514 A203813 A133487 * A188830 A103949 A057066

Adjacent sequences: A342036 A342037 A342038 * A342040 A342041 A342042

Keyword

nonn

Author

Jianing Song, Feb 26 2021

Status

approved