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

Author

R. J. Mathar, Mar 23 2007

Keywords

• nonn

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 Erdos-Selfridge classification

Crossrefs

Cf. A101253.

Programs

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 *)

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))