A108415 a(n) = 1, 2 or 3 (resp.) if prime(n) is weak, balanced or strong (resp.).

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

Offset: 2

Author

Zak Seidov, Jun 02 2005

Keywords

• nonn

Comments

n >= 2: a(n) = 1, 2 or 3 (resp.) if n-th prime is in A051635, A006562 or A051634 (resp.).

Links

• Robert Israel, Table of n, a(n) for n = 2..10000
• Wikipedia, Balanced prime

Crossrefs

Cf. A006562, A051634, A051635.

Programs

Maple

p:= 2: q:= 3: r:= 5:
for i from 2 to 200 do
  t:= q - (p+r)/2;
  A[i]:= piecewise(t<0,1,t=0,2,3);
  p:= q; q:= r; r:= nextprime(r);
od:
seq(A[i],i=2..200); # Robert Israel, Mar 25 2018

Mathematica

A108415[n_]:=2+Sign[Prime[n]-1/2(Prime[n-1]+Prime[n+1])]