OFFSET
1,1
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
FORMULA
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
PROG
CROSSREFS
KEYWORD
base,easy,nonn
AUTHOR
Amarnath Murthy, Feb 14 2002
EXTENSIONS
More terms from Vladeta Jovovic, Feb 18 2002
Edited by Ray Chandler, Apr 24 2007
STATUS
approved