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.

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A177959 n-th prime minus number of 0's in binary representation of n-th prime.

Original entry on oeis.org

1, 3, 4, 7, 10, 12, 14, 17, 22, 28, 31, 34, 38, 41, 46, 51, 58, 60, 63, 68, 69, 77, 80, 86, 93, 98, 101, 105, 107, 110, 127, 126, 132, 135, 145, 148, 154, 159, 164, 170, 176, 178, 190, 188, 193, 196, 208, 222, 224, 226, 230, 238, 238, 250, 250, 258, 264, 267, 272, 276
Offset: 1

Views

Author

Juri-Stepan Gerasimov, May 16 2010

Keywords

Crossrefs

Cf. A014499, A035193, A177687.

Programs

  • Maple
    A023416 := proc(n) a := 0 ; for d in convert(n,base,2) do if d = 0 then a := a+1 ; end if; end do; a ; end proc:
A035103 := proc(n) A023416(ithprime(n)) ; end proc:
A177959 := proc(n) ithprime(n)-A035103(n) ; end proc:
seq(A177959(n),n=1..120) ; # R. J. Mathar, May 30 2010

Formula

a(n) = A000040(n) - A035103(n).

Extensions

Corrected (39 removed, 124 replaced by 224, 126 replaced by 226) by R. J. Mathar, May 30 2010

A327785 Square array read by antidiagonals: A(n,k) = Sum_{d|n} (k/d), (n>=1, k>=0), where (m/n) is the Kronecker symbol.

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 0, 0, 3, 1, 1, 1, 1, 1, 2, 1, 1, 0, 2, 1, 0, 4, 1, 1, 1, 0, 1, 0, 0, 2, 1, 1, 2, 1, 1, 2, 0, 2, 4, 1, 1, 1, 2, 1, 1, 2, 0, 1, 3, 1, 1, 2, 0, 3, 2, 0, 2, 0, 1, 4, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 2, 1, 1, 0, 2, 3, 0, 4, 0, 0, 3, 0, 0, 6, 1
Offset: 1

Views

Author

Seiichi Manyama, Sep 25 2019

Keywords

Examples

			Square array begins:
   1, 1, 1, 1, 1, 1, 1, 1, ...
   1, 2, 1, 0, 1, 0, 1, 2, ...
   1, 2, 0, 1, 2, 0, 1, 2, ...
   1, 3, 1, 1, 1, 1, 1, 3, ...
   1, 2, 0, 0, 2, 1, 2, 0, ...
   1, 4, 0, 0, 2, 0, 1, 4, ...
   1, 2, 2, 0, 2, 0, 0, 1, ...
   1, 4, 1, 0, 1, 0, 1, 4, ...

Links

Crossrefs

Columns k=0..31 give A000012, A000005, A035185, A035186, A001227, A035187, A035188, A035189, A035185, A035191, A035192, A035193, A035194, A035195, A035196, A035197, A001227, A035199, A035200, A035201, A035202, A035203, A035204, A035205, A035188, A035207, A035208, A035186, A035210, A035211, A035212, A035213.
Cf. A215200.

Programs

  • Mathematica
    A[n_, k_] := Sum[KroneckerSymbol[k, d], {d, Divisors[n]}];
Table[A[n - k, k], {n, 1, 13}, {k, n - 1, 0, -1}] // Flatten (* Jean-François Alcover, Sep 25 2019 *)

A035255 Indices of the nonzero terms in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m= 11.

Original entry on oeis.org

1, 4, 5, 7, 9, 11, 16, 19, 20, 25, 28, 35, 36, 37, 43, 44, 45, 49, 53, 55, 63, 64, 76, 77, 79, 80, 81, 83, 89, 95, 97, 99, 100, 107, 112, 113, 121, 125, 127, 131, 133, 137, 139, 140, 144, 148, 151, 157, 167, 169, 171, 172, 175, 176, 180, 181, 185, 196, 209
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Crossrefs

Cf. A035193 (the expansion itself).

Programs

  • PARI
    m=11; select(x -> x, direuler(p=2,101,1/(1-(kronecker(m,p)*(X-X^2))-X)), 1)

Extensions

Edited and extended by Andrey Zabolotskiy, Jul 30 2020
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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