

A272232


Smallest k > 0 such that R_k//n//R_k is prime, where R_k is the repunit A002275(k) and // denotes concatenation; or 0 if no such k exists.


1



1, 9, 0, 1, 2, 1, 10, 3, 1, 1, 3, 0, 2, 3, 33, 1, 2, 1, 1, 21, 1, 2, 0, 1, 7, 48, 292, 4, 3, 1, 1, 2, 1, 0, 135, 0, 1, 0, 1, 34, 3, 3, 40, 2, 0, 1, 3, 1, 1, 32, 61, 1, 2, 1, 137, 0, 3, 1, 2, 42, 1, 14, 1, 262, 2, 22, 0, 3, 9, 2, 33, 73, 1, 3, 1, 2, 3, 0, 2, 2, 1
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OFFSET

0,2


COMMENTS

a(2) = 0 (see second comment in A258372).
a(n) = 0 if n > 0 is in A099814 (see fourth comment in A004022).
a(n) = 0 if n is of the form A000042(i)*10^j+A000042(i) for some j > i > 0, since the resulting number is divisible by A002275(k)//A000042(i).
a(n) = 0 if n is a term of A010785 with an even number of digits, since any number of the form 1..1d..d1..1 with an even number of digits d is divisible by 11.
a(n) = 1 if there exists an integer x such that n = (A002275(A004023(x))A011557(x)1)/10.
From Chai Wah Wu, Nov 07 2019: (Start)
a(n) = 0 if n has an even number of digits and is a multiple of 11. In particular, a(n) = 0 if n is a term of A056524.
a(n) = 0 if n = (10^k+1)(10^m1)/9 for some m > 0, k >= 0.
(End)


LINKS

Table of n, a(n) for n=0..80.


EXAMPLE

a(0) = 1 since 101 is prime; a(1) refers to the prime 1111111111111111111.


MATHEMATICA

Table[SelectFirst[Range[10^4], PrimeQ@ FromDigits@ Flatten@ {#, IntegerDigits@ n, #} &@ Table[1, {#}] &], {n, 0, 91}] /. k_ /; MissingQ@ k > 0 (* Michael De Vlieger, Apr 25 2016, Version 10.2 *)


PROG

(PARI) a(n) = my(k=1); while(!ispseudoprime(eval(Str((10^k1)/9, n, (10^k1)/9))), k++); k


CROSSREFS

Cf. A000042, A002275, A056524, A098814, A004023, A258372.
Sequence in context: A274186 A158336 A021530 * A110909 A197070 A197333
Adjacent sequences: A272229 A272230 A272231 * A272233 A272234 A272235


KEYWORD

nonn,base


AUTHOR

Felix FrÃ¶hlich, Apr 23 2016


EXTENSIONS

a(35)a(80) from Giovanni Resta, May 01 2016


STATUS

approved



