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

Author

K. D. Bajpai, Jul 13 2015

Keywords

• nonn
• base
• fini
• full

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A105992, A161786, A161796.

Programs

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 *)