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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A152840 a(0) = -1; a(n) = n^(n+a(n-1)) - a(n-1)^(n+a(n-1)).

Original entry on oeis.org

-1, 0, 4, -14197
Offset: 0

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Author

Keywords

Crossrefs

Programs

  • Mathematica
    lst={};a=1;Do[a=n^(n+a)-a^(n+a);AppendTo[lst,a],{n,0,3}];lst

Extensions

Indices added to definition, offset corrected - R. J. Mathar, Jan 08 2009
Definition corrected by Georg Fischer, Jun 03 2025

A162848 An alternating 2-based sum from prime(n) up to the base of the n-th Mersenne prime.

Original entry on oeis.org

0, 5, 7, 9, 18, 25, 24, 51, 120, 181, 223, 264, 1243, 1455, 3129, 5430, 5616, 7953, 10534, 10953, 24115, 24736, 27910, 49711, 54109, 57873, 111090, 215449, 276096, 329955, 540039, 1891903, 2148379, 3144261, 3495451, 7440328, 7553209, 17431240, 33667044
Offset: 1

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Author

Juri-Stepan Gerasimov, Jul 21 2009

Keywords

Comments

Define a 2-based sum S(l,u) = Sum_{j=l..u} (2 - j*(-1)^j). Then a(n) is this sum evaluated with a lower limit l = A000040(n) = prime(n) and with an upper limit u = A000043(n).

Examples

			a(1) = 2 - 2 = 0;
a(2) = 2 + 3 = 5;
a(3) = 2 + 5 = 7;
a(4) = 2 + 7 = 9;
a(5) = 2 + 11 + 2 - 12 + 2 + 13 = 18.
		

Crossrefs

Programs

  • Maple
    A152832 := proc(n) (n+1)/2-(9*(-1)^n+1)/4 ; end:
    S := proc(u) 2*u-(-1)^u*A152832(u) ; end:
    A000043 := proc(n) op(n,[ 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607,
    1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497,
    86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917 ]) ; end:
    A162848 := proc(n) S( A000043(n))-S(ithprime(n)-1) ; end: seq(A162848(n),n=1..39) ; # R. J. Mathar, Aug 14 2009

Formula

a(n) = Sum_{j=A000040(n)..A000043(n)} (2 - j*(-1)^j).

Extensions

Corrected from a(8) on by R. J. Mathar, Aug 14 2009

A152841 a(0)=1; a(n)=Floor[n^(n+a(n-1))-a(n-1)^(n+a(n-1))].

Original entry on oeis.org

1, 0, -4, -1, -115, -1
Offset: 0

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Author

Keywords

Crossrefs

Programs

  • Mathematica
    lst={};a=1;Do[a=a^(n+a)-n^(n+a);AppendTo[lst,Floor[a]],{n,0,5}];lst

Extensions

Indices added to definition, offset corrected - R. J. Mathar, Jan 08 2009
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