A353631 Arithmetic derivative of primorial base exp-function, reduced modulo 4, computed for odd numbers.

1, 1, 1, 3, 3, 3, 1, 1, 1, 3, 3, 3, 1, 1, 1, 1, 1, 1, 3, 3, 3, 1, 1, 1, 3, 3, 3, 1, 1, 1, 1, 1, 1, 3, 3, 3, 1, 1, 1, 3, 3, 3, 1, 1, 1, 1, 1, 1, 3, 3, 3, 1, 1, 1, 3, 3, 3, 1, 1, 1, 1, 1, 1, 3, 3, 3, 1, 1, 1, 3, 3, 3, 1, 1, 1, 1, 1, 1, 3, 3, 3, 1, 1, 1, 3, 3, 3, 1, 1, 1, 1, 1, 1, 3, 3, 3, 1, 1, 1, 3, 3, 3, 1, 1, 1, 1

Offset

0,4

Comments

Run lengths seem to be given by sequence 3, 3, 3, 3, 6, 3, 3, 3, 6, 3, 3, 3, 6, 3, 3, 3, 6, 3, 3, 3, 6, etc., with initially starting with four runs of length 3, followed by a run of length 6, after which periodically with always three runs of length three followed by one run of six terms (that are always 1's).

Links

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

Index entries for sequences related to primorial base

Formula

a(n) = A353630(2*n+1) = A010873(A327860(2*n+1)).

Prog

(PARI)
A353630(n) = { my(s=0, m=1, p=2, e); while(n, e = (n%p); m *= (p^e); s += (e/p); n = n\p; p = nextprime(1+p)); ((s*m)%4); };
A353631(n) = A353630(n+n+1);

Crossrefs

Odd bisection of A353630.

Cf. A010873, A327860, A353632.

Cf. also A353641.

Sequence in context: A110566 A126066 A177693 * A353641 A131289 A130974

Adjacent sequences: A353628 A353629 A353630 * A353632 A353633 A353634

Keyword

nonn,base

Author

Antti Karttunen, May 01 2022

Status

approved