cp's OEIS Frontend

A213014 Number of zeros following the initial 1 in n-th absolute difference of primes.

%I A213014 #13 Dec 13 2023 15:17:51
%S A213014 0,1,0,0,0,0,0,0,6,5,4,3,2,1,0,0,1,0,0,2,1,0,0,0,3,2,1,0,0,1,0,3,2,1,
%T A213014 0,0,6,5,4,3,2,1,0,0,1,0,0,1,0,2,1,0,1,0,0,0,0,6,5,4,3,2,1,0,2,1,0,0,
%U A213014 2,1,0,0,1,0,5,4,3,2,1,0,1,0,0,0,0,0,2,1,0,0,2,1,0,0,4,3,2,1,0,0,0,0,3,2,1,0,0
%N A213014 Number of zeros following the initial 1 in n-th absolute difference of primes.
%C A213014 Related to Gilbreath's conjecture: number of "0"s preceding the first term > 1 in the n-th row of the table A036261 (= row n of the table A036262 which starts with row 0).
%C A213014 Gilbreath's conjecture would be violated if the initial 1 would not always be followed by some number (>= 0) of "0"s and then a "2" as the first term > 1. See also A089582.
%H A213014 Robert Israel, <a href="/A213014/b213014.txt">Table of n, a(n) for n = 1..10000</a>
%p A213014 L:= [seq(ithprime(i),i=1..120)]:
%p A213014 for i from 1 to 100 do
%p A213014   L:= map(abs,L[2..-1]-L[1..-2]);
%p A213014   for j from 2 do
%p A213014     if L[j] <> 0 then R[i]:= j-2; break fi;
%p A213014   od;
%p A213014 od:
%p A213014 seq(R[i],i=1..100); # _Robert Israel_, Dec 13 2023
%o A213014 (PARI) my( p=primes(150), D(v)=vecextract(v,"^1")-vecextract(v,"^-1")); while(p=abs(D(p)),for(i=2,#p,p[i] & !print1(i-2",") & next(2));break)
%K A213014 nonn
%O A213014 1,9
%A A213014 _M. F. Hasler_, Jun 02 2012