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 1-5 of 5 results.

A292251 The 3-adic valuation of A048673(n).

Original entry on oeis.org

0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 3, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 4, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0
Offset: 1

Views

Author

Antti Karttunen, Sep 12 2017

Keywords

Crossrefs

One less than the even bisection of A292252.
Cf. also A292241, A292261.

Programs

  • Mathematica
    IntegerExponent[#, 3] & /@ Table[(Times @@ Power[If[# == 1, 1, NextPrime@ #] & /@ First@ #, Last@ #] + 1)/2 &@ Transpose@ FactorInteger@ n, {n, 120}] (* Michael De Vlieger, Sep 12 2017 *)

Formula

a(n) = A007814(1+A292250(n)).
a(n) = A007949(A048673(n)).
a(n) = A007949(3*A048673(n)) - 1.
a(n) = A292252(2n)-1.

A292241 The 3-adic valuation of A254103(n).

Original entry on oeis.org

0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 0, 2, 0, 1, 0, 3, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 4, 0, 0, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0
Offset: 0

Views

Author

Antti Karttunen, Sep 12 2017

Keywords

Crossrefs

One less than the even bisection of A292242.
Cf. also A292251, A292261.

Formula

a(n) = A007814(1+A292240(n)).
a(n) = A007949(A254103(n)).
For n >= 1, a(n) = A007949(3*A254103(n)) - 1.
For n >= 1, a(n) = A292242(2n)-1.

A292260 Binary encoding of 0-digits in ternary representation of A245612(n).

Original entry on oeis.org

0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 2, 0, 0, 3, 2, 1, 0, 16, 8, 10, 4, 1, 2, 4, 0, 12, 0, 1, 4, 6, 0, 0, 0, 41, 34, 0, 16, 33, 22, 11, 8, 2, 0, 10, 4, 21, 10, 12, 0, 5, 26, 23, 0, 4, 4, 3, 8, 5, 14, 2, 0, 5, 2, 3, 0, 146, 80, 132, 68, 43, 2, 180, 32, 0, 68, 81, 44, 12, 16, 2, 16, 33, 6, 48, 0, 9, 22, 33, 8, 54, 40, 8, 20, 11, 26, 2, 0, 126, 8, 9, 52, 0, 48, 52, 0
Offset: 0

Views

Author

Antti Karttunen, Sep 12 2017

Keywords

Crossrefs

Formula

a(n) = A291770(A245612(n)).

A292262 Number of trailing 2-digits in ternary representation of A245612(n).

Original entry on oeis.org

0, 1, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 3, 0, 1, 0, 1, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 1, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 1, 0, 1
Offset: 0

Views

Author

Antti Karttunen, Sep 12 2017

Keywords

Crossrefs

Cf. A007814, A007949, A245612, A291763, A292261 (even bisection subtracted by one).
Cf. also A292242, A292252.

Programs

Formula

a(n) = A007949(1+A245612(n)).
a(n) = A007814(1+A291763(n)).
a(0) = 0, a(1) = 1, after which a(2n) = 1 + A292261(n/2), a(2n+1) = 0.

A305297 Restricted growth sequence transform of A292260, formed from 0-digits in ternary representation of A245612(n).

Original entry on oeis.org

1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 4, 1, 1, 3, 4, 2, 1, 5, 6, 7, 8, 2, 4, 8, 1, 9, 1, 2, 8, 10, 1, 1, 1, 11, 12, 1, 5, 13, 14, 15, 6, 4, 1, 7, 8, 16, 7, 9, 1, 17, 18, 19, 1, 8, 8, 3, 6, 17, 20, 4, 1, 17, 4, 3, 1, 21, 22, 23, 24, 25, 4, 26, 27, 1, 24, 28, 29, 9, 5, 4, 5, 13, 10, 30, 1, 31, 14, 13, 6, 32, 33, 6, 34, 15, 18, 4, 1, 35, 6, 31, 36, 1, 30, 36, 1, 37
Offset: 0

Views

Author

Antti Karttunen, May 31 2018

Keywords

Comments

For all i, j: a(i) = a(j) => A292261(i) = A292261(j).

Crossrefs

Cf. also A305296, A305298.
Cf. also A304750.

Programs

  • PARI
    A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
    A048673(n) = (A003961(n)+1)/2;
    A254049(n) = A048673((2*n)-1);
    A245612(n) = if(n<2,1+n,if(!(n%2),(3*A245612(n/2))-1,A254049(A245612((n-1)/2))));
    A291770(n) = { my(s=0, b=1, d); while(n>2, if(!(n%3), s += b); b <<= 1; n \= 3); (s); };
    A292260(n) = A291770(A245612(n));
    rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
    v305297 = rgs_transform(vector(65538,n,A292260(n-1)));
    A305297(n) = v305297[1+n];
Showing 1-5 of 5 results.