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

Author

Antti Karttunen, May 01 2022

Keywords

• nonn
• base

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

Crossrefs

Odd bisection of A353630.

Cf. A010873, A327860, A353632.

Cf. also A353641.

Programs

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);

Formula

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