A069710 Primes with arithmetic mean of digits = 1 (sum of digits = number of digits).

11, 1021, 1201, 2011, 3001, 10103, 10211, 10301, 11003, 12011, 12101, 13001, 20021, 20201, 21011, 21101, 30011, 1000033, 1000213, 1000231, 1000303, 1001023, 1001041, 1001311, 1001401, 1002121, 1003003, 1003111, 1003201, 1010131

Offset: 1

Author

Amarnath Murthy, Apr 08 2002

Keywords

• nonn
• base

Comments

The sum of the digits of a prime > 3 cannot be a multiple of 3, hence no prime with 3*k digits can be here. - David Radcliffe, May 05 2015

Subsequence of primes of A061384. - Michel Marcus, May 05 2015

Links

• David Radcliffe, Table of n, a(n) for n = 1..13376

Crossrefs

Cf. A069709, A069711, A069712.

Programs

Maple

F:= proc(d,s) option remember;
  local t,r;
  if d = 1 then
    if s >= 1 and s <= 9 then {s}
    else {}
    fi
  else
    `union`(seq(map(t -> 10*t+r, procname(d-1,s-r)), r=0..min(s,9)))
  fi
end proc:
`union`(seq(select(isprime,F(i,i)), i = remove(d -> d mod 3 = 0, [$1..8]));
# if using Maple 11 or earlier, uncomment the next line
# sort(convert(%,list)); # Robert Israel, May 05 2015

Mathematica

Do[p = Prime[n]; If[ Apply[ Plus, IntegerDigits[p]] == Floor[ Log[10, p] + 1], Print[p]], {n, 1, 10^5}]

Python

from itertools import count, islice
from collections import Counter
from sympy.utilities.iterables import partitions, multiset_permutations
from sympy import isprime
def A069710_gen(): # generator of terms
    for l in count(1):
        for i in range(1,min(9,l)+1):
            yield from sorted(q for q in (int(str(i)+''.join(map(str,j))) for s,p in partitions(l-i,k=9,size=True) for j in multiset_permutations([0]*(l-1-s)+list(Counter(p).elements()))) if isprime(q))
A069710_list = list(islice(A069710_gen(),30)) # Chai Wah Wu, Nov 28 2023

Extensions

Edited and extended by Robert G. Wilson v, Apr 12 2002