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 1-3 of 3 results.

A265098 Integers n such that A138523(n) is 1 or a prime.

Original entry on oeis.org

1, 2, 3, 4, 5, 28, 32
Offset: 1

Views

Author

Altug Alkan, Dec 01 2015

Keywords

Comments

Inspired by the following triangle for the initial terms:
1! = 1.
1! + 3! = 7.
1! + 3! + 5! = 127.
1! + 3! + 5! + 7! = 5167.
1! + 3! + 5! + 7! + 9! = 368047.
This sequence is finite since 107 divides A138523(n) for all n >= 53. - Amiram Eldar, Apr 20 2017

Examples

			a(4) = 4 because 1! + 3! + 5! + 7! = 5167 is prime.
		

Crossrefs

Programs

  • Mathematica
    Select[Range@ 1000, Or[# == 1, PrimeQ@ #] &@ Sum[(2 k - 1)!, {k, #}] &] (* Michael De Vlieger, Dec 01 2015 *)
  • PARI
    lista(nn) = { print1(1, ", "); s = 0; for(k=1, nn, s += (2*k-1)!; if(ispseudoprime(s), print1(k, ", ")); ); }

A138524 a(n) = Sum_{k=1..n} (2*k)!.

Original entry on oeis.org

2, 26, 746, 41066, 3669866, 482671466, 87660962666, 21010450850666, 6423384156578666, 2439325392333218666, 1126440053169940898666, 621574841786409380258666, 403913035968392044964258666, 305292257647682252546468258666
Offset: 1

Views

Author

Leroy Quet, Mar 23 2008

Keywords

Crossrefs

Programs

  • Mathematica
    Table[Sum[(2*i)!, {i,n}], {n,15}] (* Stefan Steinerberger, Mar 25 2008 *)
    Accumulate[(2*Range[20])!] (* Harvey P. Dale, Nov 12 2016 *)
  • PARI
    for(n=1,25, print1(sum(k=1,n, (2*k)!), ", ")) \\ G. C. Greubel, Sep 29 2017
    
  • Python
    from math import factorial
    def a(n): return sum(factorial(2*k) for k in range(1, n+1))
    print([a(n) for n in range(1, 16)]) # Michael S. Branicky, Feb 26 2021

Formula

A007623(a(n)) = A163662(n). - Amiram Eldar, Apr 07 2022

Extensions

More terms from Stefan Steinerberger and Robert G. Wilson v, Mar 25 2008

A138525 a(n) = Sum_{k=0..n} (2*k)!.

Original entry on oeis.org

1, 3, 27, 747, 41067, 3669867, 482671467, 87660962667, 21010450850667, 6423384156578667, 2439325392333218667, 1126440053169940898667, 621574841786409380258667, 403913035968392044964258667
Offset: 0

Views

Author

Leroy Quet, Mar 23 2008

Keywords

Comments

Last digit is 7 for n > 2. Therefore there is no square in this sequence except 1. - Altug Alkan, Dec 01 2015

Crossrefs

Partial sums of A010050.

Programs

Extensions

More terms from Stefan Steinerberger and Robert G. Wilson v, Mar 25 2008
Showing 1-3 of 3 results.