A067180 Smallest prime with digit sum n, or 0 if no such prime exists.

0, 2, 3, 13, 5, 0, 7, 17, 0, 19, 29, 0, 67, 59, 0, 79, 89, 0, 199, 389, 0, 499, 599, 0, 997, 1889, 0, 1999, 2999, 0, 4999, 6899, 0, 17989, 8999, 0, 29989, 39989, 0, 49999, 59999, 0, 79999, 98999, 0, 199999, 389999, 0, 598999, 599999, 0, 799999, 989999, 0, 2998999, 2999999, 0, 4999999

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..1000 (first 175 terms from Robert G. Wilson v)

Formula

a(3k) = 0 for k > 1.

a(3k-2) = A067523(2k-1), a(3k-1) = A067523(2k), for all k > 1. - M. F. Hasler, Nov 04 2018

Example

a(68) = 59999999 because 59999999 is the smallest prime with digit sum = 68;
a(100) = 298999999999 because 298999999999 is the smallest prime with digit sum = 100.

Maple

g:= proc(s, d) # integers of <=d digits with sum s
  if s > 9*d then return [] fi;
  if d = 1 then return [s] fi;
  [seq(op(map(t -> j*10^(d-1)+ t, g(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(1):= 0: f(3):= 3:
map(f, [$1..100]); # Robert Israel, Dec 13 2020

Mathematica

a = Table[0, {100}]; Do[b = Apply[ Plus, IntegerDigits[ Prime[n]]]; If[b < 101 && a[[b]] == 0, a[[b]] = Prime[n]], {n, 1, 10^7} ]; a
f[n_] :=  If[n > 5 && Mod[n, 3] == 0, 0, Block[{k = 1, lmt, lst = {}, ip = IntegerPartitions[n, Round[1 + n/9], {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}]}, lmt = 1 + Length@ ip; While[k < lmt, AppendTo[lst, Select[ FromDigits@# & /@ Permutations@ ip[[k]], PrimeQ[#] &]]; k++]; Min@ Flatten@ lst]]; f[1] = 0; f[4] = 13; Array[f, 70] (* Robert G. Wilson v, Sep 28 2014 *)

Prog

(PARI) A067180(n)={if(n<2, 0, n<4, n, n%3, my(d=divrem(n, 9)); forprime(p=d[2]*10^d[1]-1, , sumdigits(p)==n&&return(p)))} \\ M. F. Hasler, Nov 04 2018

Crossrefs

Cf. A054750.

Removal of the 0 terms from this sequence leaves A067523.

Sequence in context: A336838 A051298 A069870 * A067182 A342667 A191000

Adjacent sequences: A067177 A067178 A067179 * A067181 A067182 A067183

Keyword

easy,nonn,base

Author

Amarnath Murthy, Jan 09 2002

Extensions

Edited and extended by Robert G. Wilson v, Mar 01 2002

Edited by Ray Chandler, Apr 24 2007

Status

approved