A249974 - OEIS

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

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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