A053546 Smallest prime containing a leading sequence of n ascending numbers.

11, 127, 1231, 12343, 123457, 12345623, 123456719, 1234567801, 1234567891, 1234567891003, 12345678910111, 12345678910111207, 1234567891011121309, 123456789101112131449, 12345678910111213141523, 123456789101112131415161, 123456789101112131415161717

Offset: 1

Author

Enoch Haga, Jan 16 2000

Keywords

• base
• easy
• nice
• nonn

Comments

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

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

Examples

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

Links

• T. D. Noe, Table of n, a(n) for n = 1..100 (probable primes)

Programs

Mathematica

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 *)