A331869
Numbers n for which R(n) + 4*10^floor(n/2) is prime, where R(n) = (10^n-1)/9 (repunit: A002275).
Original entry on oeis.org
1, 3, 4, 15, 76, 91, 231, 1363, 1714, 1942, 2497, 4963, 5379, 12397, 23224, 26395
Offset: 1
For n = 1, R(1) + 4*10^floor(1/2) = 5 is prime.
For n = 3, R(3) + 4*10^floor(3/2) = 151 is prime.
For n = 4, R(4) + 4*10^floor(4/2) = 1511 is prime.
For n = 15, R(15) + 4*10^floor(15/2) = 111111151111111 is prime.
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Select[Range[0, 2500], PrimeQ[(10^# - 1)/9 + 4*10^Floor[#/2]] &]
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for(n=0,9999,ispseudoprime(p=10^n\9+4*10^(n\2))&&print1(n","))
A161796
Primes with at least one digit appearing exactly five times in the decimal expansion.
Original entry on oeis.org
101111, 111119, 111121, 111191, 111211, 111611, 112111, 113111, 131111, 199999, 311111, 313333, 323333, 331333, 333233, 333323, 333331, 333337, 333383, 333433, 333533, 334333, 343333, 353333, 444443, 444449, 511111, 555557, 599999, 611111
Offset: 1
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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 100000 do p := ithprime(n) ; if isdgctm(p,5) then printf("%d,",p) ; fi; od: # R. J. Mathar, Jun 21 2009
A177999
Largest n digit prime with the most digits equal to 1.
Original entry on oeis.org
7, 11, 911, 8111, 16111, 911111, 1171111, 71111111, 131111111, 1711111111, 31111111111, 311111111111, 5111111111111, 41111111111111, 111151111111111, 5111111111111111, 11111611111111111, 191111111111111111
Offset: 1
A331868
Numbers k for which R(k) + 4*10^floor(k/2-1) is prime, where R(n) = (10^n-1)/9 (repunit: A002275).
Original entry on oeis.org
4, 147, 270, 1288, 1551, 3427
Offset: 1
For n = 4, R(4) + 4*10^floor(4/2-1) = 1151 is prime.
For n = 5, R(5) + 4*10^floor(5/2-1) = 11151 = 3^3*7*59 is not prime.
For n = 147, R(147) + 4*10^72 = 1(74)51(72) is prime, where (.) indicates how many times the preceding digit is repeated.
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Select[Range[2, 2500], PrimeQ[(10^# - 1)/9 + 4*10^Floor[#/2 - 1]] &]
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for(n=2,9999,isprime(p=10^n\9+4*10^(n\2-1))&&print1(n","))
A257937
Primes p such that one digit appears exactly six times together with a single different digit.
Original entry on oeis.org
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
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.
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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
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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 *)
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