A257937 Primes p such that one digit appears exactly six times together with a single different digit.

1111151, 1111181, 1111211, 1111711, 1114111, 1117111, 1171111, 2999999, 3233333, 3331333, 3333133, 3333233, 3333313, 3333331, 3333373, 3333383, 3333433, 3337333, 3353333, 3433333, 3733333, 4999999, 7477777, 7577777, 7727777, 7772777, 7774777, 7777727, 7778777, 7877777, 9899999, 9929999, 9999299, 9999929, 9999991

Offset

1,1

Comments

All the terms are congruent to 1 or 2 (mod 3).

In no term does the digit 0, 2, 4, 5, 6, or 8 appear six times.

Links

K. D. Bajpai, Table of n, a(n) for n = 1..35

Example

a(1) = 1111151 has exactly six 1's together with a single digit 5.
a(8) = 2999999 has exactly six 9's together with a single digit 2.

Maple

sort(select(isprime, [seq(seq(seq(d*1111111 + (a-d)*10^k, k=0..6), a={$1..9} minus {d}), d=1..9)])); # Robert Israel, Jul 13 2015

Mathematica

kQ[n_]:= Module[{d=Select[DigitCount[n], # > 0 &]}, Length[d] == 2 && Min[d] == 1 && Max[d] == 6]; Select[Table[Prime[n], {n, 1000000}], kQ]
Select[Prime[Range[80000, 400000]], MemberQ[DigitCount[#], 6] &] (* Vincenzo Librandi, Jul 14 2015 *)

Crossrefs

Cf. A105992, A161786, A161796.

Sequence in context: A035613 A038449 A262498 * A205735 A205916 A205908

Adjacent sequences: A257934 A257935 A257936 * A257938 A257939 A257940

Keyword

nonn,base,fini,full

Author

K. D. Bajpai, Jul 13 2015

Status

approved