A358602 Define u such that u(1) = k and u(n) = u(n-1) + (-1)^n*(n!) for n > 1. Terms are numbers k for which the number of consecutive values of u(i), starting at u(1) = k, that are primes reaches a new record high.

2, 3, 11, 107, 119657, 2513657, 8448047, 210336167

Offset

1,1

Links

Table of n, a(n) for n=1..8.

Example

If k = 2, u(1) = 2 is prime, and no lesser number has this property, thus 2 is a term.
If k = 11, u(1) = 11, u(2) = 11 + 2! = 13, u(3) = 13 - 3! = 7 and u(4) = 7 + 4! = 31 are primes, and no lesser number has this property, thus 11 is a term.

Prog

(PARI)
card(k)=my(s=k, c=2, p=1); while(isprime(s), p*=c; s+=if(c%2, -p, p); c++); c-=2
rec(kk=10^9)=my(r=0); forprime(k=1, kk, x=card(k); if(x>r, if(r>0, print1(", ")); print1(k); r=x))

Crossrefs

Sequence in context: A292710 A300898 A079853 * A050721 A058114 A042337

Adjacent sequences: A358599 A358600 A358601 * A358603 A358604 A358605

Keyword

nonn,more

Author

Jean-Marc Rebert, Nov 23 2022

Status

approved