A067523 The smallest prime with a possible given digit sum.

2, 3, 13, 5, 7, 17, 19, 29, 67, 59, 79, 89, 199, 389, 499, 599, 997, 1889, 1999, 2999, 4999, 6899, 17989, 8999, 29989, 39989, 49999, 59999, 79999, 98999, 199999, 389999, 598999, 599999, 799999, 989999, 2998999, 2999999, 4999999, 6999899, 8989999

Offset: 1

Author

Amarnath Murthy, Feb 14 2002

Keywords

• base
• easy
• nonn

Comments

Except for 3 no other prime has a digit sum which is a multiple of 3. Hence the possible digit sums are 2,3,4,5,7,8,10,11,13,14,16,..., etc. Conjecture: For every possible digit sum there exists a prime.

For n > 2, this is (conjecturally) the smallest prime with digit sum A001651(n). - Lekraj Beedassy, Mar 04 2009

Links

• Robert Israel, Table of n, a(n) for n = 1..667

Crossrefs

Cf. A001651. Equals A067180 with the 0 terms removed.

Programs

Maple

g:= proc(s, d) # integers of <=d digits with sum s
  local j;
  if s > 9*d then return [] fi;
  if d = 1 then return [s] fi;
  [seq(op(map(t -> j*10^(d-1)+ t, procname(s-j, d-1))), j=0..9)];
end proc:
f:= proc(n) local d, j, x, y;
  if n mod 3 = 0 then return 0 fi;
  for d from ceil(n/9) do
    if d = 1 then
      if isprime(n) and n < 10 then return n
      else next
    fi fi;
    for j from 1 to 9 do
       for y in g(n-j, d-1) do
         x:= 10^(d-1)*j + y;
         if isprime(x) then return x fi;
  od od od;
end proc:
f(3):= 3:
map(f, [2,3,seq(seq(3*i+j,j=1..2),i=1..30)]); # Robert Israel, Jan 18 2024

PARI

A067523(n)=if(n<3,n+1,A067180(n*3\/2-1)) \\ M. F. Hasler, Nov 04 2018

Formula

a(n) = min(prime(i): A007605(i) = A133223(i)). - R. J. Mathar, Nov 06 2018

Extensions

More terms from Vladeta Jovovic, Feb 18 2002

Edited by Ray Chandler, Apr 24 2007