A066068 -id:A066068 - cp's OEIS frontend

A322406 a(n) = n + n*n^n.

2, 10, 84, 1028, 15630, 279942, 5764808, 134217736, 3486784410, 100000000010, 3138428376732, 106993205379084, 3937376385699302, 155568095557812238, 6568408355712890640, 295147905179352825872, 14063084452067724991026, 708235345355337676357650, 37589973457545958193355620

Offset: 1

Ivan Stoykov, Dec 07 2018

All terms are produced by successively applying the three basic operations: exponentiation, multiplication and addition.

			a(3) = 3 + 3*3^3 = 3 + 3*27 = 8 + 81 = 84.

Muniru A Asiru, Table of n, a(n) for n = 1..380
R. L. Goodstein, Transfinite Ordinals in Recursive Number Theory, Journal of Symbolic Logic, Vol. 12, No. 4 (Dec. 1947), pp. 123-129.

Cf. A066068, A055897.

Equals 2 * A108398.

List([1..20],n->n+n*n^n); # Muniru A Asiru, Dec 07 2018

[n+n*n^n$n=1..20]; # Muniru A Asiru, Dec 07 2018

a[n_]:=n+n*n^n; Array[a, 20] (* Stefano Spezia, Dec 07 2018 *)

a(n) = n+n*n^n \\ Felix Fröhlich, Dec 07 2018

E.g.f.: exp(x) * x - LambertW(-x)/(1 + LambertW(-x))^3. - Vaclav Kotesovec, Dec 20 2018

a(12)-a(19) from Stefano Spezia, Dec 07 2018

A374964 a(n) is the smallest positive k such that -n^n == n (mod n + k).

Original entry on oeis.org

1, 1, 2, 1, 5, 1, 3, 1, 9, 1, 11, 1, 13, 1, 14, 1, 17, 1, 7, 1, 21, 1, 23, 1, 25, 1, 3, 1, 29, 1, 6, 1, 33, 1, 35, 1, 37, 1, 39, 1, 41, 1, 7, 1, 45, 1, 18, 1, 49, 1, 50, 1, 53, 1, 19, 1, 45, 1, 59, 1, 61, 1, 7, 1, 65, 1, 63, 1, 44, 1, 71, 1, 40, 1, 12, 1, 12, 1, 27, 1, 81, 1, 23, 1, 85, 1, 58, 1, 8, 1, 6, 1, 9

Offset: 1

Juri-Stepan Gerasimov, Jul 25 2024

nonn

Cf. A066068 (n^n+n).

f:= proc(n) local k;
  for k from 1 do if n &^ n + n mod (n+k) = 0 then return k fi od
end proc:
map(f, [$1..100]); # Robert Israel, Jul 30 2024

a[n_] := Module[{k = 1}, While[PowerMod[n, n, n + k] != k, k++]; k]; Array[a, 100] (* Amiram Eldar, Jul 26 2024 *)

a(n) = my(k=1); while (-Mod(n, n+k)^n != n, k++); k; \\ Michel Marcus, Jul 26 2024

def a(n): return next(k for k in range(1, n+1) if pow(n, n, n+k) == k)
print([a(n) for n in range(1, 94)]) # Michael S. Branicky, Jul 26 2024

from itertools import count
def A374964(n):
    m = n**n+n
    return next(d for d in count(1) if not m%(n+d)) # Chai Wah Wu, Aug 12 2024

a(n) = 1 for n even and a(n) <= n for n odd. - Michael S. Branicky, Jul 28 2024

a(n) + n is the least divisor > n of n^n + n. - Robert Israel, Jul 30 2024

cp's OEIS Frontend

A322406 a(n) = n + n*n^n.

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