cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Previous Showing 11-15 of 15 results.

A037064 a(n)-th prime is the smallest prime containing exactly n 6's.

Original entry on oeis.org

1, 18, 121, 859, 15226, 54070, 1071206, 3933314, 34614430, 309084622, 2792083255, 61496476037, 1214237371612, 5255429125063, 105341326636887, 458846460486827, 15441107727480784, 16660543186177748, 832868428561305574, 1494006786965549890, 14206605445888164436, 135418222271099812357
Offset: 0

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Author

Patrick De Geest, Jan 04 1999

Keywords

Links

Crossrefs

Cf. A000720, A037065, A034388.
Cf. A037052, A037054, A037056, A037058, A037060, A037062, A037066, A037068, A037070.

Programs

  • Mathematica
    (* see A037065 for f *) PrimePi[ Table[ f[n, 6], {n, 1, 12}]]

Formula

a(n) = A000720(A037065(n)). - Amiram Eldar, Jul 20 2025

Extensions

One more terms from Hans Havermann, Jun 16 2001
a(0)=1 prepended by Sean A. Irvine, Dec 06 2020
a(13)-a(21) calculated using Kim Walisch's primecount and added by Amiram Eldar, Jul 20 2025

A065589 Smallest prime beginning with exactly n 6's.

Original entry on oeis.org

2, 61, 661, 6661, 666607, 666667, 66666629, 66666667, 666666667, 6666666661, 66666666667, 6666666666629, 66666666666629, 666666666666631, 66666666666666047, 66666666666666601, 6666666666666666059, 666666666666666661, 66666666666666666601, 66666666666666666667
Offset: 0

Views

Author

Robert G. Wilson v, Nov 28 2001

Keywords

Links

Crossrefs

Cf. A037065, A065584, A065585, A065586, A065587, A065588, (this sequence), A065590, A065591, A065592.

Programs

  • Mathematica
    Do[a = Table[6, {n}]; k = 0; While[b = FromDigits[ Join[a, IntegerDigits[k] ]]; First[ IntegerDigits[k]] == 6 || !PrimeQ[b], k++ ]; Print[b], {n, 1, 17} ]
  • PARI
    a(n) = {if(n==0, return(2)); my(cs = 60*(10^n\9), pow10 = 10); for(i = 1, oo, np = cs; d = 0; while(d < pow10, np = nextprime(np + 1); d = np - cs; if(d < pow10 && digits(d)[1] != 6 || 10*d < pow10, return(np))); cs*=10; pow10*=10)} \\ David A. Corneth, Sep 06 2023

Extensions

Corrected by Don Reble, Jan 17 2007
Offset corrected by Sean A. Irvine, Sep 06 2023

A375760 Array read by rows: T(n,k) is the first prime with exactly n occurrences of decimal digit k.

Original entry on oeis.org

2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 101, 13, 2, 3, 41, 5, 61, 7, 83, 19, 1009, 11, 223, 233, 443, 557, 661, 277, 881, 199, 10007, 1117, 2221, 2333, 4441, 5557, 6661, 1777, 8887, 1999, 100003, 10111, 22229, 23333, 44449, 155557, 166667, 47777, 88883, 49999, 1000003, 101111, 1222229, 313333, 444443, 555557, 666667, 727777, 888887, 199999
Offset: 0

Views

Author

Robert Israel, Aug 27 2024

Keywords

Examples

			T(4,1) = 10111 because 10111 is the first prime with four 1's.
Array starts
      2      2       3      2      2      2      2      2      2      2
    101     13       2      3     41      5     61      7     83     19
   1009     11     223    233    443    557    661    277    881    199
  10007   1117    2221   2333   4441   5557   6661   1777   8887   1999
 100003  10111   22229  23333  44449 155557 166667  47777  88883  49999
1000003 101111 1222229 313333 444443 555557 666667 727777 888887 199999

Links

Crossrefs

Cf. A037053, A037055, A037057, A037059, A037061, A037063, A037065, A037067, A037069, A037071

Programs

  • Maple
    F:= proc(v,x) local d,y,z,L,S,SS,Cands,t,i,k;
   for d from v do
     Cands:= NULL;
     if x = 0 then SS:= combinat:-choose([$2..d-1],v)
     elif member(x,[1,3,7,9]) then SS:= combinat:-choose(d,v)
     else SS:= combinat:-choose([$2..d],v)
     fi;
     for S in SS do
       for y from 9^(d-v+1) to 9^(d-v+1)+9^(d-v)-1 do
         L:= convert(y,base,9)[1..d-v+1];
         L:= map(proc(s) if s < x then s else s+1 fi end proc, L);
         i:= 1;
         t:= 0:
         for k from 1 to d do
           if member(k,S) then t:= t + x*10^(k-1)
           else t:= t + L[i]*10^(k-1); i:= i+1;
           fi;
         od;
         Cands:= Cands, t
     od od;
     Cands:= sort([Cands]);
     for t in Cands do if isprime(t) then return t fi od;
   od
end proc:
F(0,0):= 2: F(1,2):= 2: F(1,5):= 5:
for i from 0 to 10 do
  seq(F(i,x), x=0..9)
od;
  • Mathematica
    T[n_,k_]:=Module[{p=2},While[Count[IntegerDigits[p],k]!=n, p=NextPrime[p]]; p]; Table[T[n,k],{n,0,5},{k,0,9}]//Flatten (* Stefano Spezia, Aug 27 2024 *)

A176272 Primes of the form 2(10^n-1)/3 * 10^ceiling(log_10(n+1)) + n.

Original entry on oeis.org

61, 66666667, 6666666666666666666666666666666666666666641
Offset: 1

Views

Author

Rick L. Shepherd, Apr 13 2010

Keywords

Comments

Equivalently, primes with decimal representation as n 6's with n's decimal representation concatenated. The next term is too large to include (2433 decimal digits).

Crossrefs

Cf. A176090 (corresponding n), A065589, A037065.

A178004 The n-digit prime with the largest number of 6's, the largest of these if there is more than 1. 0 if no such prime exists.

Original entry on oeis.org

0, 67, 661, 6661, 96667, 666667, 9666661, 66666667, 666666667, 6666666661, 66666666667, 669666666661, 6666676666667, 96666666666667, 696666666666661, 6966666666666661, 96666666666666661, 666666666666666661
Offset: 1

Views

Author

Lekraj Beedassy, May 17 2010

Keywords

Examples

			The largest number of 6's in 5-digit primes is 3, achieved by 16661, 26669, 46663, 56663, 60661,..., 76667, 96661, 96667. a(5) is the largest of these, 96667. - _R. J. Mathar_, Nov 23 2010

Crossrefs

Cf. A037065, A105978, A099660.
Previous Showing 11-15 of 15 results.

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