A028834 Numbers whose sum of digits is a prime.

2, 3, 5, 7, 11, 12, 14, 16, 20, 21, 23, 25, 29, 30, 32, 34, 38, 41, 43, 47, 49, 50, 52, 56, 58, 61, 65, 67, 70, 74, 76, 83, 85, 89, 92, 94, 98, 101, 102, 104, 106, 110, 111, 113, 115, 119, 120, 122, 124, 128, 131, 133, 137, 139, 140, 142, 146, 148, 151, 155, 157, 160, 164, 166, 173, 175, 179, 182

Offset: 1

Author

Armand Turpel (armand(AT)vo.lu, armand_t(AT)geocities.com)

Keywords

• nonn
• base
• easy
• nice

Examples

			89 included because 8+9 = 17, which is prime.
		

Links

• Christian N. K. Anderson, Table of n, a(n) for n = 1..25000 (terms 1..1000 from T. D. Noe)
• Christian N. K. Anderson, Ulam Spiral for a(n) <= 100000.

Crossrefs

Cf. A007953, A028835, A028842, A052018, A052019, A052020, A052021, A052022.

Cf. A010051; A046704 is a subsequence.

Complement of A104211.

Programs

Haskell

a028834 n = a028834_list !! (n-1)
a028834_list = filter ((== 1) . a010051 . a007953) [1..]
-- Reinhard Zumkeller, Nov 13 2011

Maple

a:=proc(n) local nn: nn:=convert(n,base,10): if isprime(sum(nn[j],j=1..nops(nn)))=true then n else fi end: seq(a(n),n=1..200); # Emeric Deutsch, Mar 17 2007

Mathematica

Select[Range[200],PrimeQ[Total[IntegerDigits[#]]]&]  (* Harvey P. Dale, Feb 18 2011 *)

PARI

is(n)=isprime(sumdigits(n)) \\ Felix Fröhlich, Aug 16 2014

Python

from sympy import isprime
def ok(n): return isprime(sum(map(int, str(n))))
print(list(filter(ok, range(183)))) # Michael S. Branicky, Jun 18 2021

R

require(gmp); which(sapply(1:1000, function(i) isprime(sum(floor(i/10^(0:(nchar(i)-1)))%%10)))==2) # Christian N. K. Anderson, Apr 22 2024

Sage

[x for x in range(200) if (sum(Integer(x).digits(base=10))) in Primes()] # Bruno Berselli, May 05 2014

Extensions

More terms from Scott Lindhurst (ScottL(AT)alumni.princeton.edu)