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

0,1

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

Links

Table of n, a(n) for n=0..21.

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 *)

Crossrefs

Cf. A006880, A076489, A076490.

Sequence in context: A355542 A057324 A139052 * A105226 A139021 A176038

Adjacent sequences: A076488 A076489 A076490 * A076492 A076493 A076494

Keyword

nonn,base,fini,full

Author

Labos Elemer, Oct 21 2002

Extensions

Corrected and extended by Giovanni Resta, Oct 29 2019

Status

approved