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

2, 13, 31, 1061, 1151, 1223, 1511, 1601, 2141, 2213, 2411, 3023, 3041, 3203, 3221, 4013, 4211, 5003, 5021, 6011, 6101, 7001, 10009, 10243, 10333, 10513, 10531, 10711, 11071, 11161, 11251, 11503, 11701, 12007, 12043, 12241, 12421, 12511, 12601, 13033, 13411

Offset: 1

Author

Jaroslav Krizek, Apr 16 2017

Keywords

• nonn
• base

Links

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

Crossrefs

Primes in A061385. Subsequence of A069709.

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).

Programs

Magma

[n: n in [1..100000] | IsPrime(n) and &+Intseq(n) mod #Intseq(n) eq 0 and &+Intseq(n) / #Intseq(n) eq 2];

Maple

S:= proc(d,k,flag) option remember;
  if d = 1 then
    if k >= 0 and k <= 9 then return [k]
    else return []
    fi
  fi;
  [seq(op(map(`+`, procname(d-1,k-i,0), i*10^(d-1))),i=flag..min(k,9))]
end proc:
seq(op(select(isprime,S(d,2*d,1))),d=1..5);# Robert Israel, Apr 23 2017

Mathematica

Select[Prime[Range[1600]],Mean[IntegerDigits[#]]==2&] (* Harvey P. Dale, Aug 07 2021 *)