A169818 Rank of n-th prime as defined in A177854.

0, 1, 1, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 3, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 2, 2, 2, 1, 3, 2, 2, 3, 2, 3, 2, 2, 2, 3, 3, 3, 2, 3, 2, 3, 2, 3, 2, 2, 2, 3, 3, 2, 2, 2, 2, 2, 2, 3, 3, 2, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 3, 3

Offset: 1

Author

T. D. Noe, May 28 2010

Keywords

• nonn

Comments

This notion of rank is closely related to the Erdős-Selfridge classification of primes.

Links

• T. D. Noe, Table of n, a(n) for n=1..10000

Crossrefs

For records see A177854.

Programs

Mathematica

rank[1]=0; rank[2]=0; rank[3]=1;
SetAttributes[rank,Listable];
rank[p_] := rank[p] = 1+Min[Max@@rank[First/@FactorInteger[p-1]], Max@@rank[First/@FactorInteger[p+1]]]; rank[Prime[Range[100]]]

Formula

a(A000720(A141453(n)))=1 n>1. [From R. J. Mathar, May 28 2010]