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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
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 7 19:34 EST 2021. Contains 349585 sequences. (Running on oeis4.)