A247307 Numbers of the form (4^k - 4)/k.

0, 6, 20, 63, 204, 682, 2340, 381300, 1398101, 5162220, 71582788, 1010580540, 14467258260, 3059510616420, 2573485501354569, 9938978487990060, 148764065110560900, 510526106256177860940, 117943982401427236556700, 1799331452449680632120820

Offset

1,2

Comments

Subsequence of A246445.

Generated by k = 1, 2, 3, 4, 5, 6, 7, 11, 12, 13, 15, 17, 19, 23, 28, 29, 31,. ..

This set of k contains all terms of A122781 and all primes. [It contains the primes because j^p == j (mod p) for every integer j if p is prime; see e.g. the corollary 4.4 to the Lagrange theorem in Jones et al.]

Links

Table of n, a(n) for n=1..20.

G. A. Jones and J. M. Jones, Congruences with a prime-power modulus, p 65-82 in "Elementary Number Theory", Springer Undergraduate Mathematics Series, (1988).

Example

a(9) = 1398101 because (4^12 - 4)/12 = 1398101 for k = 12.

Prog

(PARI) lista(nn) = {for (k=1, nn, va = (4^k - 4)/k; if (type(va) == "t_INT", print1(va, ", ")); ); } \\ Michel Marcus, Sep 12 2014

Crossrefs

Cf. A020136, A064535, A122781, A246445, A247033.

Sequence in context: A309294 A018808 A027107 * A279215 A318337 A264307

Adjacent sequences: A247304 A247305 A247306 * A247308 A247309 A247310

Keyword

nonn

Author

Juri-Stepan Gerasimov, Sep 11 2014

Status

approved