cp's OEIS Frontend

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

%I A126433 #18 Mar 27 2024 08:03:02
%S A126433 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,
%T A126433 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,
%U A126433 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
%N A126433 Class+ number of prime(n) according to the Erdős-Selfridge classification of primes.
%C A126433 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.
%H A126433 M. F. Hasler, <a href="/A126433/b126433.txt">Table of n, a(n) for n = 1..1000</a>
%H A126433 <a href="/index/Pri#primes_Erdos_Selfridge">Index entries for sequences related to the Erdos-Selfridge classification</a>
%p A126433 A126433 := proc(n)
%p A126433     option remember;
%p A126433     local p, pf, e, a;
%p A126433     if isprime(n) then
%p A126433         pf := ifactors(n+1)[2];
%p A126433         a := 1;
%p A126433         for e from 1 to nops(pf) do
%p A126433             p := op(1, op(e, pf));
%p A126433             if p > 3 then
%p A126433                 a := max(a, procname(p)+1);
%p A126433             end if;
%p A126433         end do;
%p A126433         a ;
%p A126433     else
%p A126433         -1;
%p A126433     end if;
%p A126433 end proc:
%p A126433 seq(A126433(ithprime(n)),n=1..100) ;
%p A126433 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
%t A126433 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 *)
%o A126433 (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))
%Y A126433 Cf. A101253.
%K A126433 nonn
%O A126433 1,6
%A A126433 _R. J. Mathar_, Mar 23 2007