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

1,9

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

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

Prog

(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)

Crossrefs

Sequence in context: A263879 A085664 A154007 * A022962 A023448 A307337

Adjacent sequences: A213011 A213012 A213013 * A213015 A213016 A213017

Keyword

nonn

Author

M. F. Hasler, Jun 02 2012

Status

approved