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A285096 Primes with integer arithmetic mean of digits = 2 in base 10.

%I A285096 #18 Jul 18 2025 16:49:42
%S A285096 2,13,31,1061,1151,1223,1511,1601,2141,2213,2411,3023,3041,3203,3221,
%T A285096 4013,4211,5003,5021,6011,6101,7001,10009,10243,10333,10513,10531,
%U A285096 10711,11071,11161,11251,11503,11701,12007,12043,12241,12421,12511,12601,13033,13411
%N A285096 Primes with integer arithmetic mean of digits = 2 in base 10.
%H A285096 Jaroslav Krizek, <a href="/A285096/b285096.txt">Table of n, a(n) for n = 1..1000</a>
%p A285096 S:= proc(d,k,flag) option remember;
%p A285096   if d = 1 then
%p A285096     if k >= 0 and k <= 9 then return [k]
%p A285096     else return []
%p A285096     fi
%p A285096   fi;
%p A285096   [seq(op(map(`+`, procname(d-1,k-i,0), i*10^(d-1))),i=flag..min(k,9))]
%p A285096 end proc:
%p A285096 seq(op(select(isprime,S(d,2*d,1))),d=1..5);# _Robert Israel_, Apr 23 2017
%t A285096 Select[Prime[Range[1600]],Mean[IntegerDigits[#]]==2&] (* _Harvey P. Dale_, Aug 07 2021 *)
%o A285096 (Magma) [n: n in [1..100000] | IsPrime(n) and &+Intseq(n) mod #Intseq(n) eq 0 and &+Intseq(n) / #Intseq(n) eq 2];
%Y A285096 Primes in A061385. Subsequence of A069709.
%Y A285096 Sequences of primes such that a(n) = k for k = 1, 2, 4, 5, 7 and 8: A069710 (k = 1), this sequence (k = 2), A285225 (k = 4), A285226 (k = 5), A285227 (k = 7), A285228 (k = 8).
%K A285096 nonn,base
%O A285096 1,1
%A A285096 _Jaroslav Krizek_, Apr 16 2017