cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

This page as a plain text file.
%I A177119 #44 Jun 20 2023 18:57:39
%S A177119 2,3,5,7,23,43,67,89,1423,2143,2341,2543,4231,4253,4523,4567,4657,
%T A177119 5647,5867,6547,6857,10243,12043,20143,20341,20431,23041,24103,25463,
%U A177119 25643,30241,32401,36457,40123,40213,40231,41023,41203,42013,43201,45263,45673,45763
%N A177119 Primes whose digits can be arranged as consecutive digits (more precisely, to form a substring of 0123456789).
%C A177119 These are the primes whose digits can be permuted to give a substring of 0123456789.
%C A177119 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_
%H A177119 Nathaniel Johnston, <a href="/A177119/b177119.txt">Table of n, a(n) for n = 1..6744</a> (full sequence)
%H A177119 G. L. Honaker, Jr. and Chris Caldwell, <a href="https://t5k.org/curios/cpage/22862.html">Prime Curios! 2543</a>
%e A177119 a(12)=2543 can be arranged as 2345.
%e A177119 109 is not a term since 019 is not a substring of 0123456789.
%p A177119 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
%t A177119 (* 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 *)
%t A177119 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 *)
%t A177119 Join[{2,3,5,7},Select[Prime[Range[57*10^5]],Union[Differences[Sort[IntegerDigits[#]]]]=={1}&]] (* _Harvey P. Dale_, Jun 20 2023 *)
%Y A177119 Cf. A000040, A001477, A156119. See A068710 for a different (and presumably infinite) version.
%K A177119 nonn,easy,fini,full,base
%O A177119 1,1
%A A177119 _G. L. Honaker, Jr._, Dec 09 2010
%E A177119 Extended by _Chris K. Caldwell_
%E A177119 Edited by _N. J. A. Sloane_, Jan 22 2011