A076491 a(2*n), a(2*n+1) is the smallest consecutive prime pairs with at least n distinct common decimal digits.

2, 3, 11, 13, 101, 103, 1031, 1033, 10223, 10243, 18379, 18397, 126079, 126097, 1206479, 1206497, 10258379, 10258397, 102346879, 102346897, 10127685439, 10127685493

Offset: 0

Author

Labos Elemer, Oct 21 2002

Keywords

• nonn
• base
• fini
• full

Comments

If the common digits were not required to be distinct, the resulting sequence would be 2, 3, 11, 13, 101, 103, 1013, 1019, 1913, 1931, 18379, 18397, 109279, 109297, 1000213, 1000231, ... - Giovanni Resta, Oct 29 2019

Crossrefs

Cf. A006880, A076489, A076490.

Programs

Mathematica

aa[n_] := Block[{p,q,cp,cq}, p = NextPrime[10^(n - 1)]; cp = IntegerDigits@ p; While[True, q = NextPrime[p]; cq = IntegerDigits[q]; If[ Length[ Intersection[cp, cq]] >= n, Break[]]; p=q; cp=cq]; {p, q}]; Flatten[aa /@ Range[0, 9]] (* Giovanni Resta, Oct 29 2019 *)

Extensions

Corrected and extended by Giovanni Resta, Oct 29 2019