A177119 Primes whose digits can be arranged as consecutive digits (more precisely, to form a substring of 0123456789).

2, 3, 5, 7, 23, 43, 67, 89, 1423, 2143, 2341, 2543, 4231, 4253, 4523, 4567, 4657, 5647, 5867, 6547, 6857, 10243, 12043, 20143, 20341, 20431, 23041, 24103, 25463, 25643, 30241, 32401, 36457, 40123, 40213, 40231, 41023, 41203, 42013, 43201, 45263, 45673, 45763

Offset: 1

Author

G. L. Honaker, Jr., Dec 09 2010

Keywords

• nonn
• easy
• fini
• full
• base

Comments

These are the primes whose digits can be permuted to give a substring of 0123456789.

This sequence has exactly 6744 terms, none of which are 3-digit, 6-digit, 9-digit, or 10-digit numbers because these are all divisible by 3. The last term is 98745623. - Chris K. Caldwell

Examples

			a(12)=2543 can be arranged as 2345.
109 is not a term since 019 is not a substring of 0123456789.
		

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..6744 (full sequence)
• G. L. Honaker, Jr. and Chris Caldwell, Prime Curios! 2543

Crossrefs

Cf. A000040, A001477, A156119. See A068710 for a different (and presumably infinite) version.

Programs

Maple

A177119:={}: for d from 1 to 5 do for s from 0 to 10-d do l:=combinat[permute]([$(s..(s+d-1))]): for k from 1 to d! do n:=add(10^(d-j)*l[k][j],j=1..d): if(isprime(n))then A177119 := A177119 union {n}: fi: od: od: od: op(A177119); # Nathaniel Johnston, Jun 23 2011

Mathematica

(* computes all terms *) Reap[Do[p=Prime[n]; If[p<10 || Union[Differences[Sort[IntegerDigits[p]]]] == {1}, Sow[p]], {n, PrimePi[98765432]}]][[2, 1]] (* T. D. Noe, Dec 10 2010 *)
lst = {}; Do[AppendTo[lst, Select[FromDigits /@ Permutations@Range[n, d + n - 1], PrimeQ[#] &]], {d, 5}, {n, 0, 10 - d}]; Union@Flatten[lst] (* Arkadiusz Wesolowski, Jan 07 2013 *)
Join[{2,3,5,7},Select[Prime[Range[57*10^5]],Union[Differences[Sort[IntegerDigits[#]]]]=={1}&]] (* Harvey P. Dale, Jun 20 2023 *)

Extensions

Extended by Chris K. Caldwell

Edited by N. J. A. Sloane, Jan 22 2011