A228144 Smallest k > n such that j*10^k + m*10^n - 1 is a prime number for at least a pair {j,m} with 0 < j < 10 and 0 < m < 10.

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 46, 47, 48, 49, 50, 51, 52, 53, 55, 55, 56, 57, 59, 59, 60, 61, 62, 63, 64, 66, 66, 67, 68, 70

Offset: 1

Author

Pierre CAMI, Aug 14 2013

Keywords

• nonn

Comments

The prime numbers are the sum of a near repdigit number starting with the digit j followed by k digits 0 and a nearepdigit number starting with the digit (m-1) followed by n digits 9 for m>1, or for m=1 a repdigit number with n digits 9.

The first primes are :

109, 1399, 13999, 139999, 1199999, 16999999, 289999999, 2099999999, 10999999999, 239999999999, 1099999999999, 34999999999999, 349999999999999, 2399999999999999.

Conjecture: there is always at least one k for each n.

Examples

			1*10^1+1*10^2=109 prime so a(1)=2.
		

Links

• Pierre CAMI, Table of n, a(n) for n = 1..4000

Crossrefs

Cf. A213790, A213883.