A316341 Characteristic function of the factorials 1!, 2!, 3!, ...

0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

Offset

0

Comments

A word that is neither morphic nor recurrent.

Links

Antti Karttunen, Table of n, a(n) for n = 0..65537

Jean-Paul Allouche, Julien Cassaigne, Jeffrey Shallit, and Luca Q. Zamboni, A Taxonomy of Morphic Sequences, arXiv preprint arXiv:1711.10807 [cs.FL], Nov 29 2017.

Index entries for characteristic functions

Formula

a(n) = 1 if A034968(n) == 1, 0 otherwise. - Antti Karttunen, Nov 07 2018

Mathematica

CoefficientList[Sum[x^k!, {k, 1, 5}], x] (* Jean-François Alcover, Nov 02 2018 *)

Prog

(PARI)
A034968(n) = { my(s=0, b=2, d); while(n, d = (n%b); s += d; n = (n-d)/b; b++); (s); };
A316341(n) = (1==A034968(n)); \\ Antti Karttunen, Nov 07 2018
first(n) = { my(res = vector(n), i = t = 1); while(t < n, res[t+1]=1; i++; t*=i); res; }; \\ David A. Corneth, Nov 07 2018
A316341(n) = for(m=2, n, (n%m || 2>n\=m) && break); n==1; \\ M. F. Hasler, Jan 19 2023
(Python)
def A316341(n):
    c, i = 1, 1
    while (c:=c*i) < n:
        i += 1
    return int(c==n) # Chai Wah Wu, Jan 11 2023

Crossrefs

Equals A012245 prefixed by 0 (up to offset and indexing convention).

Sequences mentioned in the Allouche et al. "Taxonomy" paper, listed by example number: 1: A003849, 2: A010060, 3: A010056, 4: A020985 and A020987, 5: A191818, 6: A316340 and A273129, 18: A316341, 19: A030302, 20: A063438, 21: A316342, 22: A316343, 23: A003849 minus its first term, 24: A316344, 25: A316345 and A316824, 26: A020985 and A020987, 27: A316825, 28: A159689, 29: A049320, 30: A003849, 31: A316826, 32: A316827, 33: A316828, 34: A316344, 35: A043529, 36: A316829, 37: A010060.

Cf. also A000142, A034968.

Sequence in context: A288736 A270803 A030301 * A284901 A071981 A280910

Adjacent sequences: A316338 A316339 A316340 * A316342 A316343 A316344

Keyword

nonn

Author

N. J. A. Sloane, Jul 14 2018

Extensions

Data section extended up to a(120) by Antti Karttunen, Nov 07 2018

Status

approved