A224320 Primes without "3" as a digit that remain prime when any single digit is replaced with "3".

2, 5, 7, 11, 17, 41, 47, 71, 107, 167, 179, 197, 449, 859, 1019, 1061, 1499, 2089, 16901, 47717, 56269, 86269, 11917049

Offset

1,1

Comments

No more terms < 10^13.

Links

Table of n, a(n) for n=1..23.

Carlos Rivera, Puzzle 591

Mathematica

lst = {}; n = 3; Do[If[PrimeQ[p], i = IntegerDigits[p]; If[FreeQ[i, n], t = 0; s = IntegerLength[p]; Do[If[PrimeQ@FromDigits@Insert[Drop[i, {d}], n, d], t++, Break[]], {d, s}]; If[t == s, AppendTo[lst, p]]]], {p, 86269}]; lst
p3Q[n_]:=Module[{idn=IntegerDigits[n]}, FreeQ[idn, 3] && AllTrue[ FromDigits/@ Table[ReplacePart[idn, i->3], {i, IntegerLength[n]}], PrimeQ]]; Select[Prime[Range[10^6]], p3Q] (* The program uses the function AllTrue from Mathematica version 10 *) (* Harvey P. Dale, Aug 20 2014 *)

Crossrefs

Cf. A224319, A224321-A224322. Subsequence of A038611.

Sequence in context: A265817 A045349 A338339 * A247052 A364649 A163695

Adjacent sequences: A224317 A224318 A224319 * A224321 A224322 A224323

Keyword

base,more,nonn

Author

Arkadiusz Wesolowski, Apr 03 2013

Status

approved