

A100986


Smallest k such that concatenation of r*k and 1 is a prime for all r = 1 to n but not prime for r = n+1, or smallest k such that 10*r*k+1 is a prime for all r = 1 to n but not prime for r = n+1.


9




OFFSET

1,2


COMMENTS

a(10) > 10^10.  Robert Price, Apr 02 2019


LINKS

Table of n, a(n) for n=1..9.


EXAMPLE

a(4)=33 because 331, 661, 991 and 1321 (1321=10*4*33+1) are all prime, but 1651 (1651=10*5*33+1) is not prime.  Robert Price, Apr 02 2019


MATHEMATICA

Table[k = 1;
While[! AllTrue[Table[10*r*k + 1, {r, 1, n}], PrimeQ] 
PrimeQ[10*(n + 1)*k + 1], k++]; k, {n, 1, 9}] (* Robert Price, Apr 02 2019 *)


PROG

(PARI) isok(k, n) = {for (r=1, n, if (! isprime(10*r*k+1), return (0)); ); !isprime(10*(n+1)*k+1); }
a(n) = {my(k=1); while(! isok(k, n), k++); k; } \\ Michel Marcus, Apr 03 2019


CROSSREFS

Cf. A089323.
Sequence in context: A287930 A287799 A089323 * A213141 A075732 A087690
Adjacent sequences: A100983 A100984 A100985 * A100987 A100988 A100989


KEYWORD

more,nonn


AUTHOR

Ray G. Opao, Jan 13 2005


EXTENSIONS

Corrected a(7) and added a(9) by Robert Price, Apr 02 2019


STATUS

approved



