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.

Previous Showing 11-14 of 14 results.

A093050 Exponent of 2 in (3^n-3)*2^(n-1).

Original entry on oeis.org

0, 0, 3, 2, 6, 4, 7, 6, 11, 8, 11, 10, 14, 12, 15, 14, 20, 16, 19, 18, 22, 20, 23, 22, 27, 24, 27, 26, 30, 28, 31, 30, 37, 32, 35, 34, 38, 36, 39, 38, 43, 40, 43, 42, 46, 44, 47, 46, 52, 48, 51, 50, 54, 52, 55, 54, 59, 56, 59, 58, 62, 60, 63, 62, 70, 64, 67, 66, 70
Offset: 0

Views

Author

Ralf Stephan, Mar 16 2004

Keywords

Crossrefs

Cf. A090740, A093051, A093052.
a(n) is the exponent of 2 in A016129(n-1), A024281(n), A024287(n), A066406(n)/2, A071952(n+3).

Programs

  • PARI
    a(n)=if(n<1,0,if(n%2==0,a(n/2)+2*floor((n+2)/4)+1,n-1))

Formula

Recurrence: a(2n) = a(n) + [(n+1)/2] + 1, a(2n+1) = 2n.
G.f.: Sum_{k>=0} t^2(3+2t+2t^3-t^4)/[(1+t^2)(1-t^2)^2], t=x^2^k.
a(n) = A093051(n) - 1 = A090740(n) + n - 2, for n >= 1. - Amiram Eldar, Sep 14 2024

A093051 Exponent of 2 in (3^n-3)*2^n.

Original entry on oeis.org

0, 1, 4, 3, 7, 5, 8, 7, 12, 9, 12, 11, 15, 13, 16, 15, 21, 17, 20, 19, 23, 21, 24, 23, 28, 25, 28, 27, 31, 29, 32, 31, 38, 33, 36, 35, 39, 37, 40, 39, 44, 41, 44, 43, 47, 45, 48, 47, 53, 49, 52, 51, 55, 53, 56, 55, 60, 57, 60, 59, 63, 61, 64, 63, 71, 65, 68, 67, 71
Offset: 0

Views

Author

Ralf Stephan, Mar 16 2004

Keywords

Crossrefs

a(n) is the exponent of 2 in A009613(n), A010043(n), A010046(n), A012388(n-1), A009518(n), A012391(n-1), A012457(n-1), A012458(n-1), A012461(n-1), A012462(n-2).
Cf. A093050, A093052, A090740.

Programs

  • PARI
    a(n)=if(n<1,0,if(n%2==0,a(n/2)+2*floor((n+2)/4)+1,n))

Formula

Recurrence: a(2n) = a(n) + [(n+1)/2] + 1, a(2n+1) = 2n+1.
a(n) = A090740(n) + n - 1, for n >= 1. - Amiram Eldar, Sep 14 2024

A195986 Exponent of the largest power of 2 that divides 5^n - 3^n.

Original entry on oeis.org

1, 4, 1, 5, 1, 4, 1, 6, 1, 4, 1, 5, 1, 4, 1, 7, 1, 4, 1, 5, 1, 4, 1, 6, 1, 4, 1, 5, 1, 4, 1, 8, 1, 4, 1, 5, 1, 4, 1, 6, 1, 4, 1, 5, 1, 4, 1, 7, 1, 4, 1, 5, 1, 4, 1, 6, 1, 4, 1, 5, 1, 4, 1, 9, 1, 4, 1, 5, 1, 4, 1, 6, 1, 4, 1, 5, 1, 4, 1, 7, 1, 4, 1, 5, 1, 4
Offset: 1

Views

Author

John W. Layman, Oct 12 2011

Keywords

Comments

Conjecture: a(n) = 1 if A090740 = 1, else a(n) = A090740(n)+1.

Links

Crossrefs

Cf. A005058, A007814, A090740.

Programs

  • Mathematica
    Table[IntegerExponent[5^n - 3^n, 2], {n, 100}] (* T. D. Noe, Oct 12 2011 *)
  • PARI
    A195986(n) = valuation(5^n - 3^n,2); \\ Antti Karttunen, Nov 06 2018

Formula

a(n) = A007814(A005058(n)). - Antti Karttunen, Nov 06 2018

Extensions

Name clarified by Antti Karttunen, Nov 06 2018

A091284 Exponent of 2 in -1+prime[n]^s, if s is an exponent of form 16k-8. Except a(1)=0, a(n)=1+A091283(n).

Original entry on oeis.org

0, 5, 5, 6, 5, 5, 7, 5, 6, 5, 8, 5, 6, 5, 7, 5, 5, 5, 5, 6, 6, 7, 5, 6, 8, 5, 6, 5, 5, 7, 10, 5, 6, 5, 5, 6, 5, 5, 6, 5, 5, 5, 9, 9, 5, 6, 5, 8, 5, 5
Offset: 1

Views

Author

Labos Elemer, Jan 22 2004

Keywords

Comments

Exponents of 2 in -1+p^s if the exponent s[u]=(2^u)k-(2^(u-1) comes from other sequence generated with s[u-1] exponent by adding 1 to terms of the "previous" sequence. E.g. s=256k-128 needed an addition of 6 to the terms of A091282.

Crossrefs

Cf. A023506, A007814, A091282, A091283, A090739, A090740, A090129.

Programs

  • Mathematica
    Table[{8*k-4, Table[Part[Flatten[FactorInteger [ -1+Prime[n]^(16*k-8)]], 2], {n, 2, 50}]}, {k, 1, 2}]
Previous Showing 11-14 of 14 results.

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