A358618 First differences of A258036.

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

Offset: 1

Author

Clark Kimberling and Robert G. Wilson v, Oct 31 2022

Keywords

• easy
• nonn

Comments

Conjecture: All terms belong to {1, 2, 3}. See third comment in A258036.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A258036, A358619.

Programs

Maple

P:= :
S:= NULL: count:= 0:
for i from 2 while count < 101 do
  P:= P[2..-1] - P[1..-2];
  if P[1] < 0 then S:= S,i; count:= count+1; fi;
od:
S:= [S]:
S[2..-1]-S[1..-2]; # Robert Israel, Dec 21 2022

Mathematica

nn = 210; p = Prime@ Range@ nn; t = Table[ Differences[p, n][[1]], {n, 0, nn - 1}]; s = Select[ Range@ nn, t[[#]] < 0 &]; d = Differences@ s