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 1-4 of 4 results.

A077039 Partial sums of A073579.

Original entry on oeis.org

0, -3, 2, -5, -16, -3, 14, -5, -28, 1, -30, 7, 48, 5, -42, 11, -48, 13, -54, -125, -52, -131, -214, -125, -28, 73, -30, -137, -28, 85, -42, -173, -36, -175, -26, -177, -20, -183, -350, -177, -356, -175, -366, -173, 24, -175, -386, -609, -836, -607, -374, -613, -372, -623
Offset: 1

Views

Author

Reinhard Zumkeller, Oct 21 2002

Keywords

Examples

			a(5) = 2*0+3*(-1)+5*1+7*(-1)+11*(-1) = 0-3+5-7-11 = -16.

Links

Crossrefs

Cf. A007504, A077040, A077041.

Programs

  • Haskell
    a077039 n = a077039_list !! (n-1)
a077039_list = scanl1 (+) a073579_list
-- Reinhard Zumkeller, Feb 28 2012
  • Mathematica
    Accumulate[Join[{0},If[Mod[#,4]==1,#,-#]&/@Prime[Range[2,60]]]] (* Harvey P. Dale, Feb 27 2012 *)

Formula

a(n) = -Sum_{k=2..n} A000040(k)*i^(A000040(k)+1) where i is the imaginary unit. - Anthony Browne, May 17 2016

A077040 Primes p such that abs(A077039(A049084(p))) <= p.

Original entry on oeis.org

2, 3, 5, 7, 13, 17, 19, 29, 31, 37, 43, 47, 53, 59, 61, 67, 73, 97, 101, 103, 109, 113, 127, 137, 149, 157, 181, 193, 197, 199, 281, 293, 317, 337, 349, 353, 359, 373, 397, 401, 419, 431, 439, 443, 449, 467, 479, 617, 677, 709, 773, 797, 809, 811, 821, 823, 829
Offset: 1

Views

Author

Reinhard Zumkeller, Oct 21 2002

Keywords

Links

Crossrefs

Cf. A077041, A073579, A007504, A000040.

Programs

  • Haskell
    import Data.List (findIndices)
a077040 n = a077040_list !! (n-1)
a077040_list = map (a000040 . (+ 1)) $ findIndices (<= 0) $
   zipWith (\s p -> abs s - p) a077039_list a000040_list
-- Reinhard Zumkeller, Feb 28 2012

A077041 Primes p such that abs(A077039(A049084(p))) > p.

Original entry on oeis.org

11, 23, 41, 71, 79, 83, 89, 107, 131, 139, 151, 163, 167, 173, 179, 191, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 283, 307, 311, 313, 331, 347, 367, 379, 383, 389, 409, 421, 433, 457, 461, 463, 487, 491, 499, 503, 509, 521, 523, 541
Offset: 1

Views

Author

Reinhard Zumkeller, Oct 21 2002

Keywords

Links

Crossrefs

Cf. A077040, A073579, A007504, A000040.

Programs

  • Haskell
    import Data.List (findIndices)
a077041 n = a077041_list !! (n-1)
a077041_list = map (a000040 . (+ 1)) $ findIndices (> 0) $
   zipWith (\s p -> abs s - p) a077039_list a000040_list
-- Reinhard Zumkeller, Feb 28 2012

A327855 Irregular triangle read by rows: T(n,k) = [x^k] (Sum_{i=0..prime(n)-1} (1+Legendre(i,prime(n))) * x^i)^2, for 0 <= k <= 2*prime(n)-2.

Original entry on oeis.org

1, 4, 4, 1, 4, 4, 0, 0, 1, 4, 4, 0, 4, 8, 0, 0, 4, 1, 4, 8, 8, 8, 8, 8, 0, 4, 0, 0, 0, 0, 1, 4, 4, 4, 12, 12, 12, 8, 12, 12, 12, 0, 8, 8, 8, 0, 0, 0, 4, 0, 0, 1, 4, 4, 4, 12, 8, 4, 8, 4, 4, 12, 8, 12, 24, 8, 8, 8, 0, 4, 8, 4, 8, 8, 0, 4
Offset: 1

Views

Author

Seiichi Manyama, Sep 28 2019

Keywords

Examples

			Triangle begins
[1, 4, 4],
[1, 4, 4, 0,  0],
[1, 4, 4, 0,  4,  8,  0, 0,  4],
[1, 4, 8, 8,  8,  8,  8, 0,  4,  0,  0, 0,  0],
[1, 4, 4, 4, 12, 12, 12, 8, 12, 12, 12, 0,  8,  8, 8, 0, 0, 0, 4, 0, 0],
[1, 4, 4, 4, 12,  8,  4, 8,  4,  4, 12, 8, 12, 24, 8, 8, 8, 0, 4, 8, 4, 8, 8, 0, 4],
...
------------------------------------------
1 + 4*x + 4*x^2 = 4*(x^3 - 1)/(x - 1) - 3.
1 + 4*x + 4*x^2 + 4*x^4 + 8*x^5 + 4*x^8 = 4 * (x^4 - x^3 + 2*x - 1)*(x^5 - 1)/(x - 1) + 5.
1 + 4*x + 8*x^2 + 8*x^3 + 8*x^4 + 8*x^5 + 8*x^6 + 4*x^8 = 4 * (x^2 - x + 2)*(x^7 - 1)/(x - 1) - 7.

Links

Crossrefs

Cf. A073579, A226520.

Programs

  • PARI
    forprime(p=2, 30, print(Vecrev((sum(k=0, p-1, (1+kronecker(k, p))*x^k))^2, 2*p-1),", "))

Formula

For n > 1, Sum_{k=0..2*prime(n)-2} T(n,k)*x^k == (-1)^((p - 1)/2) * p mod ((x^p - 1)/(x - 1)) where p is n-th prime.
Showing 1-4 of 4 results.

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