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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

Index entries for characteristic functions

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.)