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

1,1

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

Links

Nathaniel Johnston, Table of n, a(n) for n = 1..6744 (full sequence)

G. L. Honaker, Jr. and Chris Caldwell, Prime Curios! 2543

Example

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

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 *)

Crossrefs

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

Sequence in context: A059170 A068710 A120805 * A096265 A356271 A056041

Adjacent sequences: A177116 A177117 A177118 * A177120 A177121 A177122

Keyword

nonn,easy,fini,full,base

Author

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

Extensions

Extended by Chris K. Caldwell

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

Status

approved