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A069710
Primes with arithmetic mean of digits = 1 (sum of digits = number of digits).
14
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
1,1
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
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}]
PROG
(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
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Amarnath Murthy, Apr 08 2002
EXTENSIONS
Edited and extended by Robert G. Wilson v, Apr 12 2002
STATUS
approved