A376286 n! less trailing zeros (A004154) (mod nextprime(n)).

1, 1, 2, 1, 4, 5, 2, 9, 6, 10, 10, 3, 10, 7, 13, 11, 6, 8, 11, 15, 7, 9, 14, 13, 22, 20, 27, 4, 25, 16, 17, 7, 2, 29, 24, 10, 27, 3, 32, 18, 31, 21, 22, 15, 2, 9, 38, 26, 29, 43, 48, 10, 43, 55, 20, 51, 24, 11, 48, 2, 12, 57, 50, 1, 64, 14, 53, 8, 47

Offset

0,3

Links

Table of n, a(n) for n=0..68.

Formula

a(n) = A004154(n) mod A151800(n).

Mathematica

a[n_] := Mod[n!/10^IntegerExponent[n!, 10], NextPrime[n]]; Array[a, 69, 0](* Becomes quicker as n increases and it uses less resources. For me, this is around 2 million *)g[n_, p_] := Block[{s = 0, e = 1}, While[t = Floor[n/p^e]; t > 0, s += t; e++]; s]; f[n_] := Block[{m = NextPrime@ n, p = 1, q = 7}, p = PowerMod[2, g[n, 2] - g[n, 5], m]; p = Mod[p*PowerMod[3, g[n, 3], m], m]; While[q < n +1, p = Mod[p*PowerMod[q, g[n, q], m], m]; q = NextPrime@ q]; p]

Prog

(Python)
from functools import reduce
from sympy import nextprime
from sympy.ntheory.factor_ import digits
def A376286(n): return ((p:=nextprime(n))-1)*pow(reduce(lambda i, j:i*j%p, range(n+1, p), 1), -1, p)*pow(10, sum(digits(n, 5)[1:])-n>>2, p)%p # Chai Wah Wu, Oct 18 2024

Crossrefs

Cf. A004154, A151800.

Sequence in context: A209153 A209141 A038719 * A125751 A210860 A099492

Adjacent sequences: A376283 A376284 A376285 * A376287 A376288 A376289

Keyword

easy,base,nonn,changed

Author

Robert G. Wilson v, Sep 18 2024

Status

approved