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 1-1 of 1 results.

A160434 a(n) is the least number k such that (k-th prime after A002110(n)+1) - A002110(n) is not a prime, where A002110(n) is the n-th primorial.

Original entry on oeis.org

2, 3, 7, 11, 20, 26, 30, 37, 43, 44, 42, 64, 66, 46, 70, 87, 99, 91, 78, 95, 133, 119, 113, 133, 121, 132, 134, 151, 129, 204, 221, 164, 176, 162, 177, 169, 172, 207, 234, 237, 251, 202, 231, 294, 271, 298, 284, 257, 254, 273, 319, 267, 278, 297, 309, 350, 354
Offset: 0

Views

Author

Frederick Magata (frederick.magata(AT)web.de), May 13 2009

Keywords

Comments

The conjecture on the fortunate numbers rephrased with a(n) is a(n)>=2 for all n>=0.
More generally, is a(n) > n+1 always true, or even a(n) > log(n+1)*(n+1)?

Examples

			a(3)=11: A002110(3)+1=2*3*5+1=31. The 11 primes after 31 are 37, 41, 43, 47, 53, 59, 61, 67, 71, 73 and 79.
Subtracting 2*3*5=30 from each yields: 7, 11, 13, 17, 23, 29, 31, 37, 41, 43, 49.
These are primes except for the 11th value, which is 49=7^2.
		

Crossrefs

Programs

  • Maple
    a(n):=proc(n) option remember;local k: for k from 1 while isprime((nextprime@@k)(A002110(n)+1)-A002110(n)) do od:
    k; end;
  • PARI
    a(n) = {my(k=0, P=prod(m=1, n, prime(m))); for(m=2, oo, if(ispseudoprime(P+m), k++; if(!isprime(m), return(k)))); } \\ Jinyuan Wang, Jun 13 2020

Extensions

More terms from Jinyuan Wang, Jun 13 2020
Showing 1-1 of 1 results.