A037061 -id:A037061 - cp's OEIS frontend

A037060 a(n)-th prime is the smallest prime containing exactly n 4's.

1, 13, 86, 603, 4620, 37299, 1533327, 22568442, 23574105, 210014510, 1893613727, 17241353173, 493582559244, 13474975578701, 71056054875827, 1180956491651370, 10728352138939963, 103710009988272649, 960912626678471376, 1005142876338508545, 50686811139876408310, 288867303325879381560

Offset: 0

Patrick De Geest, Jan 04 1999

Andrew R. Booker, The Nth Prime Page.
Kim Walisch, primecount, Fast prime counting function library.

Cf. A000720, A037061, A034388.

Cf. A037052, A037054, A037056, A037058, A037062, A037064, A037066, A037068, A037070.

(* see A037061 for f *) PrimePi[ Table[ f[n, 4], {n, 1, 12}]]

a(n) = A000720(A037061(n)). - Amiram Eldar, Jul 20 2025

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

A065587 Smallest prime beginning with exactly n 4's.

Original entry on oeis.org

2, 41, 443, 4441, 44449, 444443, 44444453, 444444421, 444444443, 4444444447, 44444444441, 444444444443, 44444444444459, 444444444444421, 4444444444444423, 44444444444444411, 444444444444444413, 4444444444444444409, 44444444444444444479, 44444444444444444447

Offset: 0

Robert G. Wilson v, Nov 28 2001

M. F. Hasler, Table of n, a(n) for n = 0..200

Cf. A037061, A065584 - A065592.

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

Robert Israel, Aug 27 2024

			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

Robert Israel, Table of n, a(n) for n = 0..1009 (rows 0 to 100)

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

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;

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 *)

A178002 Largest n-digit prime with the most digits equal to 4.

Original entry on oeis.org

7, 47, 449, 4447, 44449, 444449, 7444441, 74444449, 444444443, 4444444447, 44444444441, 444444444443, 5444444444443, 84444444444449, 494444444444441, 8444444444444443, 74444444444444441, 494444444444444447

Offset: 1

Lekraj Beedassy, May 17 2010

Select first for most 4's, then take the largest.

Cf. A037061, A105980, A099658

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A037060 a(n)-th prime is the smallest prime containing exactly n 4's.

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A065587 Smallest prime beginning with exactly n 4's.

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

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A178002 Largest n-digit prime with the most digits equal to 4.

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