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A285227 Primes with integer arithmetic mean of digits = 7 in base 10.

%I A285227 #15 Nov 29 2023 16:37:54
%S A285227 7,59,1999,3889,4789,4969,4987,5689,5779,5869,6679,6949,6967,7489,
%T A285227 7669,7687,7759,7867,7993,8389,8677,8839,8893,8929,9199,9397,9649,
%U A285227 9739,9829,9883,9973,18899,19889,19979,19997,28979,29789,29879,35999,36899,37799,37889
%N A285227 Primes with integer arithmetic mean of digits = 7 in base 10.
%H A285227 Jaroslav Krizek, <a href="/A285227/b285227.txt">Table of n, a(n) for n = 1..1000</a>
%t A285227 Select[Prime@ Range@ PrimePi@ 40000, Mean@ IntegerDigits@ # == 7 &] (* _Michael De Vlieger_, Apr 22 2017 *)
%o A285227 (Magma) [n: n in [1..100000] | IsPrime(n) and &+Intseq(n) mod #Intseq(n) eq 0 and &+Intseq(n) / #Intseq(n) eq 7]
%o A285227 (Python)
%o A285227 from itertools import count, islice
%o A285227 from collections import Counter
%o A285227 from sympy.utilities.iterables import partitions, multiset_permutations
%o A285227 from sympy import isprime
%o A285227 def A285227_gen(): # generator of terms
%o A285227     yield 7
%o A285227     for l in count(2):
%o A285227         for i in range(1,10):
%o A285227             yield from sorted(q for q in (int(str(i)+''.join(map(str,j))) for s,p in partitions(7*l-i,m=l-1,k=9,size=True) for j in multiset_permutations([0]*(l-1-s)+list(Counter(p).elements()))) if isprime(q))
%o A285227 A285227_list = list(islice(A285227_gen(),30)) # _Chai Wah Wu_, Nov 29 2023
%Y A285227 Primes from A061424. Subsequence of A069709.
%Y A285227 Sequences of primes such that a(n) = k for k = 1, 2, 4, 5, 7 and 8: A069710 (k = 1), A285096 (k = 2), A285225 (k = 4), A285226 (k = 5), this sequence (k = 7), A285228 (k = 8).
%K A285227 nonn,base
%O A285227 1,1
%A A285227 _Jaroslav Krizek_, Apr 19 2017