A271628 Primes that are the sum of the digits of the numbers from 1 to n, for some n.

3, 73, 109, 127, 433, 1009, 1117, 1801, 2017, 2089, 2143, 2467, 2503, 2791, 3079, 3331, 3583, 4159, 4519, 4663, 4951, 5437, 5581, 5923, 6121, 6301, 6553, 7039, 7561, 8353, 8623, 8821, 9001, 9199, 9631, 9811, 10837, 11719, 12637, 13177, 13249, 13627, 14401, 15391

Offset: 1

Author

Paolo P. Lava, Apr 11 2016

Keywords

• nonn
• easy
• base

Examples

			The sum of the digits of 1 and 2 is a prime: 1 + 2 = 3.
The sum of the digits of the number from 1 to 16 is a prime: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 1 + 0 + 1 + 1 + 1 + 2 + 1 + 3 + 1 + 4 + 1 + 5 + 1 + 6 = 73.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A037123, A271626.

Programs

Maple

with(numtheory): P:=proc(q) local a,b,c,k,n; a:=0;
for n from 0 to q do b:=0; c:=n; for k from 1 to ilog10(n)+1 do b:=b+(c mod 10); c:=trunc(c/10); od; a:=a+b;
if isprime(a) then print(a); fi; od; end: P(10^6);

Mathematica

Select[Accumulate@ Map[Total@ IntegerDigits@ # &, Range[0, 1200]], PrimeQ] (* Michael De Vlieger, Apr 11 2016 *)

PARI

lista(nn) = for (n=1, nn, if (isprime(p=sum(k=1, n, sumdigits(k))), print1(p, ", "))); \\ Michel Marcus, Apr 11 2016