A238854 Largest right-truncatable, reversible prime in base n.

23, 53, 449, 191, 1171, 30671, 5827, 3733, 901687, 10357, 834469, 3043427, 5430889, 4060019, 498061, 34763, 118248433, 62344463, 218555173, 4463351, 114607657, 7903613, 14523874693, 211675817, 32814697, 93375223, 162466979, 8052409793, 12006877873

Offset: 3

Author

Stanislav Sykora, Mar 07 2014

Keywords

• nonn
• base
• hard

Comments

See A238850, A238851, A238852, A238853 for the finite lists of such numbers in four bases selected as examples. A sequence conceptually similar to this one, but for right-truncatable (not reversible!) primes is A023107. The present, more restrictive, condition leads to smaller numbers which can be evaluated in reasonable time for much higher n values.

Examples

			a(4) = 53 because it is a prime which in base 4 reads 311_b4, its reverse 113_b4 (decimal 23) is also a prime, the same holds for all its base-4 prefixes (31_b4 and 3_b4), and it is the largest natural having these properties.
		

Links

• Stanislav Sykora, Table of n, a(n) for n = 3..390
• Stanislav Sykora, PARI/GP scripts for genetic threads, with code and comments.

Crossrefs

Cf. Full in base 10: A238850, 16: A238851, 100: A238852, 256: A238853.

Cf. In base n: A238855 (totals), A238856 (maximum digits), A238857 (m-digits counts).

Cf. A007500, A023107, A024770, A237600, A237601, A237602.

Programs

PARI

See the link.