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

2,2

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

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])]

Crossrefs

Cf. A006562, A051634, A051635.

Sequence in context: A287561 A046924 A015710 * A278572 A136644 A111963

Adjacent sequences: A108412 A108413 A108414 * A108416 A108417 A108418

Keyword

nonn

Author

Zak Seidov, Jun 02 2005

Status

approved