A067523 - OEIS

%I #24 Jan 18 2024 11:36:55

%S 2,3,13,5,7,17,19,29,67,59,79,89,199,389,499,599,997,1889,1999,2999,

%T 4999,6899,17989,8999,29989,39989,49999,59999,79999,98999,199999,

%U 389999,598999,599999,799999,989999,2998999,2999999,4999999,6999899,8989999

%N The smallest prime with a possible given digit sum.

%C 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.

%C For n > 2, this is (conjecturally) the smallest prime with digit sum A001651(n). - _Lekraj Beedassy_, Mar 04 2009

%H Robert Israel, <a href="/A067523/b067523.txt">Table of n, a(n) for n = 1..667</a>

%F a(n) = min(prime(i): A007605(i) = A133223(i)). - _R. J. Mathar_, Nov 06 2018

%p g:= proc(s, d) # integers of <=d digits with sum s

%p   local j;

%p   if s > 9*d then return [] fi;

%p   if d = 1 then return [s] fi;

%p   [seq(op(map(t -> j*10^(d-1)+ t, procname(s-j, d-1))), j=0..9)];

%p end proc:

%p f:= proc(n) local d, j, x, y;

%p   if n mod 3 = 0 then return 0 fi;

%p   for d from ceil(n/9) do

%p     if d = 1 then

%p       if isprime(n) and n < 10 then return n

%p       else next

%p     fi fi;

%p     for j from 1 to 9 do

%p        for y in g(n-j, d-1) do

%p          x:= 10^(d-1)*j + y;

%p          if isprime(x) then return x fi;

%p   od od od;

%p end proc:

%p f(3):= 3:

%p map(f, [2,3,seq(seq(3*i+j,j=1..2),i=1..30)]); # _Robert Israel_, Jan 18 2024

%o (PARI) A067523(n)=if(n<3,n+1,A067180(n*3\/2-1)) \\ _M. F. Hasler_, Nov 04 2018

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

%K base,easy,nonn

%O 1,1

%A _Amarnath Murthy_, Feb 14 2002

%E More terms from _Vladeta Jovovic_, Feb 18 2002

%E Edited by _Ray Chandler_, Apr 24 2007