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A090534 Least n-digit prime in which every two-digit string is also a prime, or 0 if no such number exists. (n-1 two-digit string primes occur.) 3
2, 11, 113, 1117, 11113, 111119, 1111379, 11111117, 111111113, 1111111973, 11111111113, 111111111379, 1111111111717, 11111111111719, 111111111111713, 1111111111111319, 11111111111111119, 111111111111111131 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Conjecture: sequence is infinite. Notes: (1) If n==1 (mod 3) then in most cases a(n) is a permutation of (n-1), 1's and a 7, else a(n) is a digit permutation of (n-1) ones and a 3; (2) Obviously all the digits except the most significant one must be odd.

The least potential candidate, lpc(n), is of the form (10^n-1)/9. The following is a(n)-lpc(n): 1, 0, 2, 6, 2, 8, 268, 6, 2, 862, 2, 268, 606, 608, 602, 208, 8, 20, 0, 20, 68, 600, 0, 2, 606, .... - Robert G. Wilson v, May 12 2014

LINKS

Robert G. Wilson v, Table of n, a(n) for n = 1..100

EXAMPLE

a(5) = 11113 in which 11,11,11,13 are the two-digit string primes.

MATHEMATICA

fQ[p_] := Block[{id = IntegerDigits@ p}, Union@ PrimeQ[ FromDigits@# & /@ Partition[id, 2, 1]] == {True}]; f[n_] := Block[{p = NextPrime[(10^n - 1)/9 - 1]}, While[! fQ@ p, p = NextPrime@ p]; p]; f[1] = 2; Array[ f, 19] (* Robert G. Wilson v, May 12 2014 *)

CROSSREFS

Cf. A242377.

Sequence in context: A145163 A205073 A069574 * A286869 A181168 A269082

Adjacent sequences:  A090531 A090532 A090533 * A090535 A090536 A090537

KEYWORD

base,nonn

AUTHOR

Amarnath Murthy, Dec 08 2003

EXTENSIONS

More terms from David Wasserman, Dec 21 2005

STATUS

approved

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Last modified November 17 18:24 EST 2019. Contains 329241 sequences. (Running on oeis4.)