cp's OEIS Frontend

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

%I A069710 #28 Nov 28 2023 22:00:23
%S A069710 11,1021,1201,2011,3001,10103,10211,10301,11003,12011,12101,13001,
%T A069710 20021,20201,21011,21101,30011,1000033,1000213,1000231,1000303,
%U A069710 1001023,1001041,1001311,1001401,1002121,1003003,1003111,1003201,1010131
%N A069710 Primes with arithmetic mean of digits = 1 (sum of digits = number of digits).
%C A069710 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
%C A069710 Subsequence of primes of A061384. - _Michel Marcus_, May 05 2015
%H A069710 David Radcliffe, <a href="/A069710/b069710.txt">Table of n, a(n) for n = 1..13376</a>
%p A069710 F:= proc(d,s) option remember;
%p A069710   local t,r;
%p A069710   if d = 1 then
%p A069710     if s >= 1 and s <= 9 then {s}
%p A069710     else {}
%p A069710     fi
%p A069710   else
%p A069710     `union`(seq(map(t -> 10*t+r, procname(d-1,s-r)), r=0..min(s,9)))
%p A069710   fi
%p A069710 end proc:
%p A069710 `union`(seq(select(isprime,F(i,i)), i = remove(d -> d mod 3 = 0, [$1..8]));
%p A069710 # if using Maple 11 or earlier, uncomment the next line
%p A069710 # sort(convert(%,list)); # _Robert Israel_, May 05 2015
%t A069710 Do[p = Prime[n]; If[ Apply[ Plus, IntegerDigits[p]] == Floor[ Log[10, p] + 1], Print[p]], {n, 1, 10^5}]
%o A069710 (Python)
%o A069710 from itertools import count, islice
%o A069710 from collections import Counter
%o A069710 from sympy.utilities.iterables import partitions, multiset_permutations
%o A069710 from sympy import isprime
%o A069710 def A069710_gen(): # generator of terms
%o A069710     for l in count(1):
%o A069710         for i in range(1,min(9,l)+1):
%o A069710             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))
%o A069710 A069710_list = list(islice(A069710_gen(),30)) # _Chai Wah Wu_, Nov 28 2023
%Y A069710 Cf. A069709, A069711, A069712.
%K A069710 nonn,base
%O A069710 1,1
%A A069710 _Amarnath Murthy_, Apr 08 2002
%E A069710 Edited and extended by _Robert G. Wilson v_, Apr 12 2002