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.

A124375 Numbers k such that A003422(k+1)/2 is prime.

Original entry on oeis.org

2, 3, 4, 7, 8, 9, 10, 29, 75, 162, 270, 272, 353, 720, 1795, 3732, 4768, 9315, 12220, 41531
Offset: 1

Views

Author

Alexander Adamchuk, Oct 28 2006

Keywords

Comments

Sum_{i=0..k} i! = k! + !k = A003422(k+1), where !k is left factorial !k = Sum_{i=0..k-1} i! = A003422(k). Left factorials are even for k > 1. Corresponding primes of the form (k! + !k)/2 = (a(n)! + !a(n))/2 are listed in A124374(n) = {2, 5, 17, 2957, 23117, 204557, 2018957, 4578979328975537786697650470157, ...}.
A near-duplicate of A100614: a(n) = A100614(n) - 1. - Ryan Propper, Feb 07 2008

Crossrefs

Programs

  • Mathematica
    f=0;Do[f=f+n!;If[PrimeQ[f/2],Print[{n,f/2}]],{n,0,353}]
    Flatten[Position[Accumulate[(Range[0,12220]!)]/2,?PrimeQ]]-1 (* _Harvey P. Dale, Jul 02 2019 *)

Extensions

More terms from Ryan Propper, Feb 07 2008
a(20) from Jinyuan Wang, Mar 20 2021

A124374 Primes of the form !(k + 1)/2 = Sum_{i=0..k} i!/2.

Original entry on oeis.org

2, 5, 17, 2957, 23117, 204557, 2018957, 4578979328975537786697650470157, 12572230784049013026617689884981971446439568309146114097251787122217783800812199225999909965168264460210470157
Offset: 1

Views

Author

Alexander Adamchuk, Oct 28 2006

Keywords

Comments

Sum_{i=0..k} i! = k! + !k = A003422(k+1), where !k is left factorial !k = Sum_{i=0..k-1} i! = A003422(k). Left factorials are even for k > 1. Corresponding numbers k such that Sum_{i=0..k} i!/2 = A003422(k+1)/2 is prime are listed in A124375(n) = {2, 3, 4, 7, 8, 9, 10, 29, 75, 162, 270, 272, 353, ...}.

Crossrefs

Programs

  • Mathematica
    f=0;Do[f=f+n!;If[PrimeQ[f/2],Print[{n,f/2}]],{n,0,353}]

Formula

a(n) = A003422(A124375(k) + 1)/2.

A288451 Numbers n such that !n + 7 is prime.

Original entry on oeis.org

0, 3, 4, 5, 7, 10, 12, 20, 37, 52, 73, 149, 304, 540, 2135, 7112, 7436, 9357
Offset: 1

Views

Author

Serge Batalov, Jul 14 2017

Keywords

Comments

At present the terms >= 2135 are only probable primes.
Expected to be finite, similar to Živković (1999).

Examples

			4 is a term, because 0! + 1! + 2! + 3! + 7 = 17 is prime.
		

Crossrefs

Programs

Showing 1-3 of 3 results.