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.

1, 3, 21, 33, 1083, 2541, 822486, 51282, 1296060612

Offset: 1

Author

Ray G. Opao, Jan 13 2005

Keywords

• more
• nonn

Comments

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

Examples

			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
		

Crossrefs

Cf. A089323.

Programs

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 *)

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

Extensions

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