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.
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); };
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).
Cf. A084558 (partial sums).
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.
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