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

1,2

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.

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.

Links

Table of n, a(n) for n=1..25.

Example

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.

Crossrefs

Cf. A000040, A262373.

Sequence in context: A112386 A160693 A167442 * A124991 A176009 A068836

Adjacent sequences: A249971 A249972 A249973 * A249975 A249976 A249977

Keyword

nonn,base

Author

Vladimir Shevelev, Sep 20 2015

Status

approved