A338366 a(n) = smallest positive number k with all digits equal such that the concatenation k||n||k is prime, or -1 if no such k exists.

1, 3, 7, 1, 11, 1, 7777, 3, 1, 1, 9, -1, 7, 33, 99, 1, 3, 1, 1, 9, 1, 11, -1, 1, 7, 3, 7777777777, 1111, 111, 1, 1, 3, 1, -1, 3, 33, 1, 3, 1, 77777777777777, 111, 3, 1111111111111111111111111111111111111111, 3, -1, 1, 3, 1, 1, 999, 7, 1, 11, 1, 7, -1, 33, 1, 3, 3, 1, 3, 1

Offset: 0

Author

N. J. A. Sloane, Nov 08 2020

Keywords

• sign
• base

Comments

See A090287 for more information.

From Robert Price, Sep 20 2023: (Start)

For a(366), k is a string of 8441 1's.

The sequence then continues: 77, 1, 1, 3, 1, 1, 9, 7777777, 1, 11, 3, 1, 11, 9, 77, 11111, 1, 1, 33333, 3, 7, 9, 3, 1, 77, 1, 1, 9, 7777777777 until a(396) where k is a sequence of 269 1's.

The sequence then continues: 9, 777, 11, 9, 1, 7, 3, 7, 1, 11, 1, 1, 9, 9, 1111, 3, 999, 77777, 99, 7, 7, 3, 7, -1, 3, 1, 11, 77, 1, 77, 3, 1, 7, 3, 3, 1, 111111, 1, 7, 99, 7, 1111, 9, 1, 1, 11, 1, 7777777, 11, 1, 1111, 3, 1111, 7, 3, 7, 11, 3, 1, 1, 111, 3, 1, 3, 3, 1, 33, 9, 11, 33, 3, 7, 3, 3, 7, 99, 1, 1, 11, 3, 1, 9, 7, 77, 9, 1, 1, 3, 1, 7777, 33, 3, 1, 33, 3, 77, 77, 9, 1, 3, 33, 11111, 9, 9. (End)

Examples

			a(3) = 1 because 131 is prime.
a(4) = 11 because 11411 is prime, and all of 141, 242, 343, ..., 949 are composite.
		

Links

• Robert Price, Table of n, a(n) for n = 0..365
• Index entries for primes involving decimal expansion of n

Crossrefs

Cf. A090287.

Related sequences: A010785, A068695, A091088, A228323, A228325, A336893, A338712 (see also the Index link above).

Extensions

More terms from Alois P. Heinz, Nov 08 2020