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Revision History for A341999

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A341999

a(n) = 1 if the k-th arithmetic derivative is nonzero for all k >= 0, otherwise 0.
(history; published version)

#19 by Michael De Vlieger at Thu Jan 05 18:30:47 EST 2023

STATUS

proposed

approved

#18 by Antti Karttunen at Thu Jan 05 15:51:10 EST 2023

STATUS

editing

proposed

#17 by Antti Karttunen at Thu Jan 05 15:49:16 EST 2023

FORMULA

a(n) = 1 - A328308(n) , and for n >= 1, a(n) = A342023(n) + A359546(n). - Antti Karttunen, Jan 05 2023

#16 by Antti Karttunen at Thu Jan 05 15:46:15 EST 2023

FORMULA

a(n) = 1 - A328308(n) = A342023(n) + A359546(n). - Antti Karttunen, Jan 05 2023

CROSSREFS

Cf. A099308 (positions of zeros), A099309 (of ones), A328308 (one's complement), A342023, A359542 (inverse Möbius transform), A359546.

#15 by Antti Karttunen at Thu Jan 05 08:05:23 EST 2023

CROSSREFS

Cf. A099308 (positions of zeros), A099309 (of ones), A328308 (one's complement), A359542 (inverse Möbius transform).

#14 by Antti Karttunen at Thu Jan 05 07:21:57 EST 2023

FORMULA

a(n) = 1 - A328308(n). - Antti Karttunen, Jan 05 2023

CROSSREFS

Cf. A099308 (positions of zeros), A099309 (of ones), A328308 (one's complement).

STATUS

approved

editing

#13 by Susanna Cuyler at Mon Mar 01 17:55:21 EST 2021

STATUS

proposed

approved

#12 by Antti Karttunen at Sun Feb 28 23:33:04 EST 2021

STATUS

editing

proposed

#11 by Antti Karttunen at Sun Feb 28 23:32:45 EST 2021

FORMULA

For all n >= 1, 0, a(A099309(n)) = a(A100716(n)) = 1.

For all n > 0, a(n) = [A256750(n) < 1].

For all n > 1, 0, a(n) >= [A129251(n)>0], i.e., if A129251(n) is nonzero, then certainly a(n) = 1.

For all n > 1, a(n) = [A256750(n) < 1].

#10 by Antti Karttunen at Sun Feb 28 23:30:32 EST 2021

FORMULA

For all n > 1, a(n) >= [A129251(n)>0], i.e., if A129251(n) is nonzero, then certainly a(n) = 1. Similarly, a(n) >= [A341997(n)>1].

For all n > 1, a(n) >= [A341997(n) > 1].

For all n > 1, a(n) = [A256750(n) < 1].

CROSSREFS

Cf. A003415, A100716, A129251, A256750, A341996, A341997.

STATUS

proposed

editing