A249953 Primes with distinct digits: a(n) is the least prime > a(n-1) such that a(n-1) and a(n) share just one digit.

13, 17, 19, 29, 59, 79, 89, 97, 107, 139, 157, 163, 179, 239, 241, 257, 263, 271, 283, 307, 349, 367, 389, 409, 421, 439, 457, 461, 479, 509, 521, 547, 563, 571, 593, 613, 647, 653, 691, 701, 739, 751, 769, 809, 821, 839, 857, 863, 937, 941, 953, 967, 983, 1049, 1237, 1409, 1523, 1607

Offset: 1

Author

Zak Seidov, Dec 05 2014

Keywords

• nonn
• base
• fini
• full

Comments

The last term is a(163) = 102437.

Links

• Zak Seidov, Table of n, a(n) for n = 1..163

Crossrefs

Subsequence of A029743.

Cf. A030284.

Programs

Mathematica

a249953[n_Integer] := Module[{t = {1}, i},
  Do[If[And[DuplicateFreeQ[IntegerDigits[Prime[i]]],
     Length[Intersection[IntegerDigits[Last@t],
        IntegerDigits[Prime[i]]]] == 1], True;
t = Append[t, Prime[i]]], {i, 1, n}]; Rest[t]]; a249953[120000] (* Michael De Vlieger, Dec 14 2014 *)
lp1d[n_]:=Module[{p=NextPrime[n]},While[Length[Intersection[ IntegerDigits[ n],IntegerDigits[p]]]!=1||!DuplicateFreeQ[ IntegerDigits[ p]],p= NextPrime[ p]];p]; NestList[lp1d,13,60] (* Harvey P. Dale, May 31 2019 *)