A241499 a(n)= k is the number of consecutive primes of the form 10^d - prime(n), 10^(d+1)- prime(n),...,10^(d+k-1)- prime(n) where d is the number of decimal digits of prime(n).

0, 3, 1, 1, 1, 0, 2, 0, 0, 2, 0, 0, 1, 0, 2, 2, 3, 0, 0, 4, 0, 0, 1, 2, 1, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0

Offset

1,2

Comments

The growth of a(n) is very slow. The smallest prime p such that the number of consecutive primes is equal to n for n = 0, 1, 2,... is given by the sequence b(n) = 2, 5, 17, 3, 71, 535673,... (hard).

Links

Table of n, a(n) for n=1..87.

Example

a(2) = 3 because prime(2)= 3 => 10^1-3 = 7, 10^2-3 = 97 and 10^3-3 = 997  with three consecutive primes, but 10^4-3 = 9997 = 13*769 is composite.

Maple

with(numtheory):for n from 1 to 100 do:p:=ithprime(n):c:=0:ii:=0:l:=length(p):for k from l to 100 while(ii=0) do:q:=10^k - p:if type(q, prime)=true then c:=c+1:else ii:=1:fi:od: printf(`%d, `, c):od:

Crossrefs

Cf. A000040.

Sequence in context: A321444 A338889 A104608 * A236774 A110245 A230003

Adjacent sequences: A241496 A241497 A241498 * A241500 A241501 A241502

Keyword

nonn,base

Author

Michel Lagneau, Apr 24 2014

Status

approved