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

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, 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, 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

Offset: 1

Author

M. F. Hasler, Jun 02 2012

Keywords

• nonn

Comments

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).

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.

Links

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

Programs

Maple

L:= [seq(ithprime(i),i=1..120)]:
for i from 1 to 100 do
  L:= map(abs,L[2..-1]-L[1..-2]);
  for j from 2 do
    if L[j] <> 0 then R[i]:= j-2; break fi;
  od;
od:
seq(R[i],i=1..100); # Robert Israel, Dec 13 2023

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)