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 A341999 a(n) = 1 if the k-th arithmetic derivative is nonzero for all k >= 0, otherwise 0. 5
 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0 COMMENTS Characteristic function of A099309. LINKS Antti Karttunen, Table of n, a(n) for n = 0..65537 FORMULA a(n) = 1 if n is in A100716 or ends there by repeated applications of A003415, otherwise a(n) = 0 (when n instead reaches 0 by such iteration). For all n, a(n) >= A341996(n). For all n > 0, a(A099309(n)) = a(A100716(n)) = 1. For all n > 0, a(n) = [A256750(n) < 1]. For all n > 0, a(n) >= [A129251(n)>0], i.e., if A129251(n) is nonzero, then certainly a(n) = 1. For all n > 1, a(n) >= [A341997(n) > 1]. PROG (PARI) A003415checked(n) = if(n<=1, 0, my(f=factor(n), s=0); for(i=1, #f~, if(f[i, 2]>=f[i, 1], return(0), s += f[i, 2]/f[i, 1])); (n*s)); A341999(n) = if(!n, n, while(n>1, n = A003415checked(n)); (!n)); CROSSREFS Cf. A003415, A100716, A129251, A256750, A341996, A341997. Cf. A099308 (positions of zeros), A099309 (of ones). Sequence in context: A144596 A188187 A341996 * A118685 A244063 A080343 Adjacent sequences:  A341996 A341997 A341998 * A342000 A342001 A342002 KEYWORD nonn AUTHOR Antti Karttunen, Feb 28 2021 STATUS approved

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Last modified June 18 20:45 EDT 2021. Contains 345121 sequences. (Running on oeis4.)