A129474 Primes of Erdos-Selfridge class 14+.

1704961513, 7281416041, 7638227617, 9462536833, 11934730597, 13237911481, 13282423003, 13522629793, 13942983841, 14185279861, 16029089501, 16221987853, 17434233041, 18171787987, 19639505461, 20717555041

Offset

1,1

Comments

Primes of class r (or r+) are by definition the primes p for which p + 1 has all factors of a lower class < r, but at least one factor of class r - 1. See A005113 for more information.

a(1..149) calculated using A090468 up to 37.5e9, which gives A129474(150) > 75e9.

Links

M. F. Hasler, Table of n, a(n) for n = 1..149

Formula

{ a(n) } = { p = 2*m*A090468(k)-1 | k=1,2,3... and m=1,2,3... such that p is prime and m has no factor of class > 13+ }

Example

a(1) = A005113[14] = 1704961513 = -1+2*852480757, where 852480757 = A090468[2]

Prog

(PARI) class(n, s=1) = { if(!isprime(n), 0, if(!(n=factor(n+s)[, 1]) || n[ #n]<=3, 1, for(i=2, #n, n[1]=max(class(n[i], s)+1, n[1])); n[1]))};
nextclass(a, s=1, p, n=[])={if(!p, p=nextprime(a[ #a]+1)); print("producing primes of class ", 1+class(a[1], s), ["+", "-"][1+(s<0)], " up to 2*", p); for(i=1, #a, for(k=1, p/a[i], if(isprime(2*k*a[i]-s), n=concat(n, 2*k*a[i]-s)))); vecsort(n)};
A129474=nextclass(A090468, 1)

Crossrefs

Cf. A005113, A005105-A005108, A081633-A081639, A084071, A090468, A129475.

Sequence in context: A186175 A202573 A071372 * A204347 A228376 A015411

Adjacent sequences: A129471 A129472 A129473 * A129475 A129476 A129477

Keyword

nonn

Author

M. F. Hasler, Apr 16 2007

Status

approved