The On-Line Encyclopedia of Integer Sequences (OEIS)

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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.
(history; published version)

#47 by Amiram Eldar at Tue Nov 07 03:16:42 EST 2023

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reviewed

approved

#46 by Stefano Spezia at Tue Nov 07 01:08:28 EST 2023

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proposed

reviewed

#45 by Michel Marcus at Tue Nov 07 01:07:46 EST 2023

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editing

proposed

#44 by Michel Marcus at Tue Nov 07 01:06:39 EST 2023

NAME

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.

REFERENCES

E. Trost, Primzahlen, Verlag Birkhauser, Birkhäuser, 1953, Theorems 20 - 21.

STATUS

approved

editing

#43 by Joerg Arndt at Fri Oct 23 02:33:49 EDT 2015

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proposed

approved

#42 by Jon E. Schoenfield at Fri Oct 23 01:45:00 EDT 2015

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editing

proposed

#41 by Jon E. Schoenfield at Fri Oct 23 01:44:56 EDT 2015

COMMENTS

The sequence is infinite. Indeed, by [SierpinskiSierpiński] (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. Sierpinski, Sierpiński, Sur l'existence de nombres premiers avec une suite arbitraire de chiffres initiaux, Le Matematiche Catania, 1951.

E. Trost, Primzahlen, Verlag Birkhauser, 1953, Theorems 20 - 21.

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approved

editing

#40 by N. J. A. Sloane at Sun Sep 20 11:27:00 EDT 2015

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editing

approved

#39 by N. J. A. Sloane at Sun Sep 20 11:26:58 EDT 2015

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.

we obtain the number 113 and the reverse number

s=311. The smallest prime ending with 311 is

2311. So a(6)=2311.

KEYWORD

nonn,new,base

STATUS

approved

editing

#38 by N. J. A. Sloane at Sun Sep 20 11:25:54 EDT 2015

STATUS

editing

approved