A005111 -id:A005111 - cp's OEIS frontend

A126805 "Class-" (or "class-minus") number of prime(n) according to the Erdős-Selfridge classification of primes.

1, 1, 1, 1, 2, 1, 1, 1, 3, 2, 2, 1, 2, 2, 4, 2, 3, 2, 3, 2, 1, 2, 3, 3, 1, 2, 2, 3, 1, 2, 2, 2, 2, 4, 2, 2, 2, 1, 4, 3, 4, 2, 2, 1, 2, 3, 2, 2, 3, 2, 3, 2, 2, 2, 1, 3, 4, 2, 4, 2, 5, 2, 2, 3, 2, 3, 3, 2, 4, 3, 3, 5, 3, 3, 2, 3, 2, 3, 2, 2, 3, 2, 3, 1, 2, 2, 2, 2, 4, 3, 4, 3, 1, 2, 4, 3, 3, 2, 3, 2, 2, 5, 3, 3, 2

Offset: 1

R. J. Mathar, Feb 23 2007

This gives the "class-" number as opposed to the "class+" number. Not to be confused with the "class-number" of quadratic form theory.

a(n)=1 if A000040(n) is in A005109, a(n)=2 if A000040(n) is in A005110, a(n)=3 if A000040(n) is in A005111 etc.

Cf. A056637.

A126805 := proc(n)
    option remember;
    local p, pe, a;
    if isprime(n) then
        a := 1;
        for pe in ifactors(n-1)[2] do
            p := op(1, pe);
            if p > 3 then
                a := max(a, procname(p)+1);
            end if;
        end do;
        a ;
    else
        -1;
    end if;
end proc:
seq(A126805(ithprime(n)),n=1..100) ;

a [n_] := a[n] = Module[{p, pf, e, res}, If[PrimeQ[n], pf = FactorInteger[n-1]; res = 1; For[e = 1, e <= Length[pf], e++, p = pf[[e, 1]]; If[p > 3, res = Max[res, a[p]+1]]]; Return[res], -1]]; Table[a[Prime[n]], {n, 1, 105}] (* Jean-François Alcover, Dec 13 2013, translated from Maple *)

A126805(n) = { if( n>0, n=-prime(n)); if(( n=factor(-1-n)[,1] ) & n[ #n]>3, vecsort( vector( #n, i, A126805(-n[i]) ))[ #n]+1, 1) } \\ M. F. Hasler, Apr 16 2007

a(n) = max { a(p)+1 ; prime(p) is > 3 and divides prime(n)-1 } union { 1 } - M. F. Hasler, Apr 16 2007

A101231 a(n) = n-th prime of Erdős-Selfridge classification n-.

Original entry on oeis.org

2, 29, 67, 179, 941, 4079, 20389, 65267, 224563, 978863, 6448979, 47247763, 309550999, 2150787839, 13925010299

Offset: 1

Jonathan Vos Post, Dec 15 2004

Diagonalization of the Erdős-Selfridge classification of primes.

			a(1) = 2 because 2 is the first element of A005109.
a(2) = 29 because 29 is the 2nd element of A005110.
a(3) = 67 because 67 is the 3rd element of A005111.
a(4) = 179 because 179 is the 4th element of A005112.

R. K. Guy, Unsolved Problems in Number Theory, A18.

Cf. A056637, A005109, A005110, A005111, A005112, A005113, A081424, A081425, A081426, A081427, A081429.

More terms from R. J. Mathar, May 02 2007

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A126805 "Class-" (or "class-minus") number of prime(n) according to the Erdős-Selfridge classification of primes.

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A101231 a(n) = n-th prime of Erdős-Selfridge classification n-.

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