

A241499


a(n)= k is the number of consecutive primes of the form 10^d  prime(n), 10^(d+1) prime(n),...,10^(d+k1) prime(n) where d is the number of decimal digits of prime(n).


0



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
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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 => 10^13 = 7, 10^23 = 97 and 10^33 = 997 with three consecutive primes, but 10^43 = 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



