A087571 Smallest prime which has the form of the concatenation n, n-1, n-2, n-3, .., n-k for some k < n, or 0 if no such prime exists.

0, 2, 3, 43, 5, 0, 7, 0, 0, 109, 11, 0, 13, 0, 0, 0, 17, 0, 19, 0, 0, 2221, 23, 2423, 25242322212019181716151413, 0, 2726252423, 0, 29, 0, 31, 0, 0, 3433, 0, 0, 37, 0, 0, 0, 41, 4241, 43, 0, 0, 4645444342414039, 47, 4847464544434241, 0, 0, 5150494847

Offset

1,2

Comments

a(p) = p. Conjecture; There are infinitely many composite numbers n such that a(n) is nonzero.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..506

Example

a(10) = 109 a concatenation of 10 and 9.
a(6) = 0 as no number in the sequence 6,65,654,6543,65432,654321 is prime.

Mathematica

Parallelize[Table[Module[{k=m, c, lst}, c=Range[k, 1, -1]; lst=Table[FromDigits[Flatten[IntegerDigits/@Take[c, n]]], {n, k}]; SelectFirst[ lst, PrimeQ]]/.Missing["NotFound"]->0, {m, 100}]] (* Harvey P. Dale, Apr 20 2025 *)

Crossrefs

Sequence in context: A379922 A334533 A196874 * A126018 A257467 A255092

Adjacent sequences: A087568 A087569 A087570 * A087572 A087573 A087574

Keyword

base,nonn

Author

Amarnath Murthy, Sep 16 2003

Extensions

Corrected and extended by Gabriel Cunningham (gcasey(AT)mit.edu), Sep 21 2003

Status

approved