A249974 a(1)=1; otherwise, find the first digit from the left in a(n-1) which is 1, 3, 7 or 9. Omitting the digits before this one, we reverse the remaining digits, obtaining s, say. Then a(n) is the smallest prime which ends with s and has not already appeared.

1, 11, 211, 311, 2113, 2311, 5113, 6311, 6113, 8311, 11113, 131111, 3111131, 21311113, 63111131, 31311113, 31111313, 531311113, 1131111313, 273131111311, 311311113137, 5731311113113, 6311311113137, 12731311113113, 2331131111313721

Offset: 1

Author

Vladimir Shevelev, Sep 20 2015

Keywords

• nonn
• base

Comments

The sequence is infinite. Indeed, by [Sierpiński] (see also Theorem 21 in [Trost]) for given decimal digits c_1..c_m such that c_m equals 1,3,7 or 9, there are infinitely many primes ending with c_1..c_m.

Examples

			Let n=6. Since a(5)=2113, then, omitting 2, we obtain the number 113 whose reverse is s=311. The smallest prime ending with 311 is 2311. So a(6)=2311.
		

References

• W. Sierpiński, Sur l'existence de nombres premiers avec une suite arbitraire de chiffres initiaux, Le Matematiche Catania, 1951.
• E. Trost, Primzahlen, Verlag Birkhäuser, 1953, Theorems 20 - 21.

Crossrefs

Cf. A000040, A262373.