cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A353630 Arithmetic derivative of primorial base exp-function, reduced modulo 4.

Original entry on oeis.org

0, 1, 1, 1, 2, 1, 1, 3, 0, 3, 3, 3, 2, 1, 3, 1, 0, 1, 3, 3, 2, 3, 1, 3, 0, 1, 1, 1, 2, 1, 1, 1, 2, 1, 3, 1, 0, 3, 3, 3, 2, 3, 3, 1, 0, 1, 1, 1, 2, 3, 1, 3, 0, 3, 1, 1, 2, 1, 3, 1, 2, 1, 3, 1, 0, 1, 3, 3, 2, 3, 1, 3, 0, 1, 1, 1, 2, 1, 1, 3, 0, 3, 3, 3, 2, 1, 3, 1, 0, 1, 3, 1, 0, 1, 1, 1, 2, 3, 1, 3, 0, 3, 1, 1, 2, 1
Offset: 0

Views

Author

Antti Karttunen, May 01 2022

Keywords

Links

Crossrefs

Cf. A010873, A166486 (parity of terms), A276086, A327860, A328572, A353493, A353640.
Cf. A353631, A353632 (bisections).
Cf. also A353486.

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); };

Formula

a(n) = A010873(A327860(n)).
a(n) = A353493(A276086(n)).
a(n) = A010873(A328572(n)*A353640(n)). [Note that all terms of A328572 are odd]

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

Original entry on oeis.org

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

Views

Author

Antti Karttunen, May 01 2022

Keywords

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

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)).

A353642 Even bisection of A353640.

Original entry on oeis.org

0, 1, 2, 1, 0, 1, 2, 3, 0, 3, 2, 3, 0, 1, 2, 1, 2, 1, 0, 3, 2, 3, 0, 3, 2, 1, 0, 1, 2, 1, 2, 1, 0, 1, 2, 1, 0, 3, 2, 3, 0, 3, 2, 1, 0, 3, 0, 3, 2, 1, 0, 1, 2, 1, 0, 3, 2, 3, 0, 3, 0, 3, 2, 3, 0, 3, 2, 1, 0, 1, 2, 1, 0, 3, 2, 1, 2, 1, 0, 3, 2, 3, 0, 3, 2, 1, 0, 1, 2, 1, 2, 1, 0, 1, 2, 1, 0, 3, 2, 3, 0, 3, 2, 1, 0, 1
Offset: 0

Views

Author

Antti Karttunen, May 01 2022

Keywords

Links

Crossrefs

Cf. A000035, A010873, A342002, A353640, A353641.
Cf. also A353632.

Programs

  • PARI
    A353640(n) = { my(s=0, m=1, p=2, e); while(n, e = (n%p); m *= p^(e>0); s += (e/p); n = n\p; p = nextprime(1+p)); ((s*m)%4); };
A353642(n) = A353640(n+n);

Formula

a(n) = A353640(2*n) = A010873(A342002(2*n)).
For all n >= 0, A000035(a(n)) = A000035(n). [Preserves parity]
Showing 1-3 of 3 results.

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