A126433 Class+ number of prime(n) according to the Erdős-Selfridge classification of primes.

1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 3, 2, 2, 1, 1, 2, 2, 2, 1, 4, 2, 2, 2, 2, 2, 3, 1, 2, 3, 1, 2, 2, 2, 2, 3, 3, 3, 2, 3, 2, 3, 1, 3, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 2, 3, 4, 2, 3, 3, 3, 2, 3, 2, 2, 2, 3, 1, 3, 3, 3, 3, 2, 3, 1, 2, 2, 4, 2, 3, 2, 3, 3, 2, 3, 3, 2, 2, 2, 3, 3, 3, 3, 2, 2, 3, 3

Offset

1,6

Comments

a(n)=1 if A000040(n) is in A005105. a(n)=2 if A000040(n) is in A005106, a(n)=3 if in A005107 etc. The locations of records are implicit in A005113.

Links

M. F. Hasler, Table of n, a(n) for n = 1..1000

Index entries for sequences related to the Erdős-Selfridge classification

Maple

A126433 := proc(n)
    option remember;
    local p, pf, e, a;
    if isprime(n) then
        pf := ifactors(n+1)[2];
        a := 1;
        for e from 1 to nops(pf) do
            p := op(1, op(e, pf));
            if p > 3 then
                a := max(a, procname(p)+1);
            end if;
        end do;
        a ;
    else
        -1;
    end if;
end proc:
seq(A126433(ithprime(n)), n=1..100) ;
A126433 := n -> if n>0 then A126433(-ithprime(n)) else numtheory[factorset](1-n); if % subset{2, 3} then 1 else 1+max(seq(A126433(-i), i=%)) fi fi; map(%, [$1..999]); # M. F. Hasler, Apr 02 2007

Mathematica

classPlus[p_] := classPlus[p] = If[f = FactorInteger[p + 1][[All, 1]]; q = Last[f]; q == 2 || q == 3, 1, Max[classPlus /@ f] + 1]; classPlus /@ Prime /@ Range[105] (* Jean-François Alcover, Jun 24 2013 *)

Prog

(PARI) A126433(n) = { if( n>0, n=-prime(n)); n=factor(1-n)[, 1]; if( n[ #n]>3, vecsort( vector( #n, i, A126433(-n[i]) ))[ #n]+1, 1) }; vector(999, i, A126433(i))

Crossrefs

Cf. A101253.

Sequence in context: A023124 A023120 A167970 * A386310 A237271 A336041

Adjacent sequences: A126430 A126431 A126432 * A126434 A126435 A126436

Keyword

nonn

Author

R. J. Mathar, Mar 23 2007

Status

approved