A231712 a(n) = n^n + n - 1.

0, 1, 5, 29, 259, 3129, 46661, 823549, 16777223, 387420497, 10000000009, 285311670621, 8916100448267, 302875106592265, 11112006825558029, 437893890380859389, 18446744073709551631, 827240261886336764193, 39346408075296537575441, 1978419655660313589123997

Offset: 0

Author

Jaroslav Krizek, Nov 12 2013

Keywords

• nonn

Comments

Supersequence of A187605 (primes of the form n^n + n - 1).

Numbers n such that a(n) = prime: 2, 3, 19, 30, 535, 1551, ..., another term > 2300 (see A058912 and A187605).

Also generalization of the problem: "What is the minimum length of a text consisting only of the first n letters of the alphabet and containing all possible n-tuples (no blanks)?" (see Puzzleup link). Example for n = 3, length of text a(3) = 29: AAABAACABBABCACBACCBBBCBCCCAA, all triples (AAA, AAB, ..., CCC) occurring exactly once. - Jörg Zurkirchen, Sep 06 2014

Links

• Jaroslav Krizek, Table of n, a(n) for n = 0..50
• PuzzleUp, Problem No. 04: Four Letters, August 20, 2014.

Crossrefs

Cf. A187605, A058912, A066279, A066068.

Programs

Magma

[n^n+n-1 : n in [0..20]]; // Wesley Ivan Hurt, Sep 23 2014

Maple

A231712:=n->n^n+n-1: seq(A231712(n), n=0..20); # Wesley Ivan Hurt, Sep 23 2014

Mathematica

Join[{0}, Table[n^n + n - 1, {n, 18}]]

PARI

a(n)=n^n+n-1 \\ Edward Jiang, Sep 06 2014

Formula

a(n) = A066279(n) - 2 = A066068(n) - 1.

E.g.f.: 1/(1 + LambertW(-x)) + (x-1)*exp(x). - Alois P. Heinz, Jun 15 2018