A285226 -id:A285226 - cp's OEIS frontend

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

Jaroslav Krizek, Apr 16 2017

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

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).

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

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

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

A285225 Primes with integer arithmetic mean of digits = 4 in base 10.

Original entry on oeis.org

17, 53, 71, 1069, 1087, 1249, 1429, 1447, 1483, 1609, 1627, 1663, 1753, 1861, 1933, 1951, 2239, 2293, 2347, 2383, 2437, 2473, 2617, 2671, 2707, 2833, 2851, 3049, 3067, 3229, 3319, 3373, 3391, 3463, 3517, 3571, 3607, 3643, 3733, 3823, 3931, 4057, 4093, 4129

Offset: 1

Jaroslav Krizek, Apr 16 2017

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

Primes in A061387. 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), this sequence (k = 4), A285226 (k = 5), A285227 (k = 7), A285228 (k = 8).

[n: n in [1..100000] | IsPrime(n) and &+Intseq(n) mod #Intseq(n) eq 0 and &+Intseq(n) / #Intseq(n) eq 4];

Select[Prime[Range[600]],Mean[IntegerDigits[#]]==4&] (* Harvey P. Dale, Jun 11 2024 *)

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

Original entry on oeis.org

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

Jaroslav Krizek, Apr 19 2017

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

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).

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

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

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

A285228 Primes with integer arithmetic mean of digits = 8 in base 10.

Original entry on oeis.org

79, 97, 6899, 8699, 8969, 9689, 9887, 49999, 68899, 69997, 77899, 78889, 78979, 79699, 79987, 85999, 88789, 88897, 88969, 89599, 89689, 89779, 89797, 89959, 89977, 94999, 95989, 96799, 96979, 96997, 97789, 97879, 97987, 98689, 98779, 98869, 98887, 99679, 99787

Offset: 1

Jaroslav Krizek, Apr 19 2017

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

Primes from A061425. 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), A285227 (k = 7), this sequence (k = 8).

[n: n in [1..100000] | IsPrime(n) and &+Intseq(n) mod #Intseq(n) eq 0 and &+Intseq(n) / #Intseq(n) eq 8];

Select[Prime@ Range@ PrimePi[10^5], Mean@ IntegerDigits@ # == 8 &] (* Michael De Vlieger, Apr 22 2017 *)

from itertools import count, islice
from collections import Counter
from sympy.utilities.iterables import partitions, multiset_permutations
def A285228_gen(): # generator of terms
    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((l<<3)-i,m=l-1,k=9,size=True) for j in multiset_permutations([0]*(l-1-s)+list(Counter(p).elements()))) if isprime(q))
A285228_list = list(islice(A285228_gen(),30)) # Chai Wah Wu, Nov 28 2023

A285095 Corresponding values of arithmetic means of digits of primes from A069709.

Original entry on oeis.org

2, 3, 5, 7, 1, 2, 4, 5, 2, 5, 4, 7, 4, 5, 8, 8, 1, 2, 4, 4, 2, 1, 2, 4, 5, 4, 4, 4, 5, 2, 5, 2, 4, 4, 4, 5, 4, 5, 4, 4, 4, 5, 7, 1, 5, 2, 2, 4, 4, 5, 4, 4, 2, 4, 5, 4, 5, 5, 4, 5, 4, 5, 4, 5, 5, 4, 5, 4, 5, 5, 5, 1, 2, 2, 4, 4, 5, 2, 2, 4, 4, 5, 4, 4, 5, 4, 5

Offset: 1

Jaroslav Krizek, Apr 16 2017

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

Cf. A069709 (primes with integer arithmetic mean of digits in base 10).

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), A285227 (k = 7), A285228 (k = 8).

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

cp's OEIS Frontend

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

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Magma

Maple

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A285225 Primes with integer arithmetic mean of digits = 4 in base 10.

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Magma

Mathematica

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

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Magma

Mathematica

Python

A285228 Primes with integer arithmetic mean of digits = 8 in base 10.

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Magma

Mathematica

Python

A285095 Corresponding values of arithmetic means of digits of primes from A069709.

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Magma