login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

First differences of A258036.
3

%I #16 Dec 21 2022 12:53:48

%S 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,

%T 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,

%U 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

%N First differences of A258036.

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

%H Robert Israel, <a href="/A358618/b358618.txt">Table of n, a(n) for n = 1..10000</a>

%p P:= <seq(ithprime(i),i=1..250)>:

%p S:= NULL: count:= 0:

%p for i from 2 while count < 101 do

%p P:= P[2..-1] - P[1..-2];

%p if P[1] < 0 then S:= S,i; count:= count+1; fi;

%p od:

%p S:= [S]:

%p S[2..-1]-S[1..-2]; # _Robert Israel_, Dec 21 2022

%t 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

%Y Cf. A258036, A358619.

%K easy,nonn

%O 1,1

%A _Clark Kimberling_ and _Robert G. Wilson v_, Oct 31 2022