A238850 Right-truncatable reversible primes in base 10.

2, 3, 5, 7, 31, 37, 71, 73, 79, 311, 313, 373, 733, 739, 797, 3733

Offset: 1

Author

Stanislav Sykora, Mar 06 2014

Keywords

• nonn
• fini
• full
• base
• easy

Comments

In a general base b, a number qualifies as a member iff: (i) it is a prime, (ii) when its digits in base b are reversed, it is still a prime, and (iii) when, in base b, it has more than one digit and the least significant one is dropped, the remaining prefix has the same properties. This implies that any base-b prefix of such a number, no matter how many right-side digits are truncated, is still a right-truncatable reversible prime. Sequences of this type appear to be all finite (see A238854, A238855, and A238856, used as examples).

This particular sequence is for base b = 10.

See also A238854 for comments on a more general context.

Examples

			739 is a member because it is a prime and so is 937, as well as the pair (73, 37) and 7.
		

Links

• Stanislav Sykora, PARI/GP scripts for genetic threads, with code and comments.

Crossrefs

In base 16: A238851, 100: A238852, 256: A238853.

In base n: A238854 (largest), A238855 (totals), A238856 (maximum digits), A238857 (m-digit counts).

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

Programs

PARI

See the link.