A161796 -id:A161796 - cp's OEIS frontend

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

K. D. Bajpai, Jul 13 2015

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.

			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.

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

Cf. A105992, A161786, A161796.

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

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 *)

A161848 Primes with at least one digit appearing exactly three times in the decimal expansion.

Original entry on oeis.org

1117, 1151, 1171, 1181, 1511, 1777, 1811, 1999, 2111, 2221, 2333, 2777, 2999, 3313, 3323, 3331, 3343, 3373, 3433, 3533, 3733, 3833, 4111, 4441, 4447, 4999, 5333, 5557, 6661, 7177, 7333, 7477, 7577, 7717, 7727, 7757, 7877, 8111, 8887, 8999, 9199, 9929

Offset: 1

Ki Punches, Jun 20 2009

Sequence is probably infinite.

			2333, 3313, 3833 all repeat some digit 3 three times.

Cf. A161786, A161796.

isdgctm := proc(n,d) local dgs,a,i ; dgs := convert(n,base,10) ; a := [seq(0,j=0..9)] ;
for i in dgs do a := subsop(i+1=op(i+1,a)+1,a) ; od: if convert(a,set) intersect {d} <> {} then true; else false; fi; end:
for n from 1 to 2000 do p := ithprime(n) ; if isdgctm(p,3) then printf("%d,",p) ; fi; od: # R. J. Mathar, Jun 21 2009

Edited and corrected by R. J. Mathar, Jun 21 2009

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

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