A129477 Primes p of Erdos-Selfridge class 6+ with largest prime factor of p+1 not of class 5+.

2146141, 2182897, 2954773, 3199813, 3224317, 3285577, 3383593, 3505933, 3555121, 3567373, 3653137, 3775417, 3864037, 4250977, 4298533, 4328053, 4493773, 4504651, 4519981, 4572037, 4647277, 4692637, 4719061, 4726537

Offset

1,1

Comments

See A129470

Links

Table of n, a(n) for n=1..24.

Example

a(1) = 2146141 = -1+2*1021*1051 = A129469[6] is a prime of class 6+ since 2146141+1 has prime factor 1021=A081633[1]=A005113[5] of class 5+, but the largest prime factor of 2146141+1 is 1051=A005107[65] of class 3+.

Prog

(PARI) class(n, s=1)={n=factor(n+s)[, 1]; if(n[ #n]<=3, 1, for(i=2, #n, n[1]=max(class(n[i], s)+1, n[1])); n[1])}; a129477(n=100, p=1, a=[])={local(f, a5=A005113[5]); p=max(p, a5*nextprime(a5+1)*2-1); while( #a<n, until( #f>2 & f[ #f-1] >= a5 & 5 > class(f[ #f]), f=factor(1+p=nextprime(p+1))[, 1]); forstep( i=#f-1, 2, -1, if( 6 < f[1] = max( f[1], 1+class( f[i] )), next(2))); if( f[1] == 6, a=concat(a, p); print(#a, " ", p))); a}

Crossrefs

Subsequence of A129470; see also A129471-A129473, A129478, A129469, A005113, A005105-A005108, A081633-A081634.

Sequence in context: A367364 A367602 A237140 * A235930 A178227 A154709

Adjacent sequences: A129474 A129475 A129476 * A129478 A129479 A129480

Keyword

easy,nonn

Author

M. F. Hasler, Apr 17 2007

Status

approved