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A069710
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Primes with arithmetic mean of digits = 1 (sum of digits = number of digits).
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14
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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MAPLE
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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
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MATHEMATICA
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Do[p = Prime[n]; If[ Apply[ Plus, IntegerDigits[p]] == Floor[ Log[10, p] + 1], Print[p]], {n, 1, 10^5}]
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PROG
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(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))
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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