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

7, 59, 1999, 3889, 4789, 4969, 4987, 5689, 5779, 5869, 6679, 6949, 6967, 7489, 7669, 7687, 7759, 7867, 7993, 8389, 8677, 8839, 8893, 8929, 9199, 9397, 9649, 9739, 9829, 9883, 9973, 18899, 19889, 19979, 19997, 28979, 29789, 29879, 35999, 36899, 37799, 37889

Offset: 1

Author

Jaroslav Krizek, Apr 19 2017

Keywords

• nonn
• base

Links

• Jaroslav Krizek, Table of n, a(n) for n = 1..1000

Crossrefs

Primes from A061424. Subsequence of A069709.

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).

Programs

Magma

[n: n in [1..100000] | IsPrime(n) and &+Intseq(n) mod #Intseq(n) eq 0 and &+Intseq(n) / #Intseq(n) eq 7]

Mathematica

Select[Prime@ Range@ PrimePi@ 40000, Mean@ IntegerDigits@ # == 7 &] (* Michael De Vlieger, Apr 22 2017 *)

Python

from itertools import count, islice
from collections import Counter
from sympy.utilities.iterables import partitions, multiset_permutations
from sympy import isprime
def A285227_gen(): # generator of terms
    yield 7
    for l in count(2):
        for i in range(1,10):
            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))
A285227_list = list(islice(A285227_gen(),30)) # Chai Wah Wu, Nov 29 2023