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Smallest prime containing a leading sequence of n ascending numbers.
5

%I #30 Jul 06 2019 14:24:49

%S 11,127,1231,12343,123457,12345623,123456719,1234567801,1234567891,

%T 1234567891003,12345678910111,12345678910111207,1234567891011121309,

%U 123456789101112131449,12345678910111213141523,123456789101112131415161,123456789101112131415161717

%N Smallest prime containing a leading sequence of n ascending numbers.

%C The Magma Calculator (http://magma.maths.usyd.edu.au/calc/) verified each of the 100 terms in the table as prime. - _Jon E. Schoenfield_, Aug 24 2009

%C Can this sequence be proved to be infinite, a sort of Dirichlet's Theorem in reverse? - _Charles R Greathouse IV_, Jul 23 2011

%H T. D. Noe, <a href="/A053546/b053546.txt">Table of n, a(n) for n = 1..100</a> (probable primes)

%e a(6) = 12345623 is the smallest prime beginning with the string 123456.

%t sp[n_]:=Module[{m=1,np},np=NextPrime[n*10^m];While[Floor[np/10^m] != n,m++;np=NextPrime[n*10^m]];np]; sp/@Table[FromDigits[ Flatten[ IntegerDigits/@ Range[x]]],{x,20}] (* _Harvey P. Dale_, May 22 2016 *)

%K base,easy,nice,nonn

%O 1,1

%A _Enoch Haga_, Jan 16 2000