A061387 -id:A061387 - cp's OEIS frontend

A061388 Sum of digits = 5 times number of digits.

5, 19, 28, 37, 46, 55, 64, 73, 82, 91, 159, 168, 177, 186, 195, 249, 258, 267, 276, 285, 294, 339, 348, 357, 366, 375, 384, 393, 429, 438, 447, 456, 465, 474, 483, 492, 519, 528, 537, 546, 555, 564, 573, 582, 591, 609, 618, 627, 636, 645, 654, 663, 672, 681

Offset: 1

Amarnath Murthy, May 03 2001

			186 is a term as the arithmetic mean of the digits is (1+8+6)/3 = 5.

Delbert L. Johnson, Table of n, a(n) for n = 1..20000

Cf. A061383, A061384, A061385, A061386, A061387, A061423, A061424, A061425.

[ n: n in [1..700] | &+Intseq(n) eq 5*#Intseq(n) ];  // Bruno Berselli, Jun 30 2011

Select[Range[685],Total[x=IntegerDigits[#]]==5*Length[x] &]

More terms from Larry Reeves (larryr(AT)acm.org), May 16 2001

A061423 Sum of digits = 6 times number of digits.

Original entry on oeis.org

6, 39, 48, 57, 66, 75, 84, 93, 189, 198, 279, 288, 297, 369, 378, 387, 396, 459, 468, 477, 486, 495, 549, 558, 567, 576, 585, 594, 639, 648, 657, 666, 675, 684, 693, 729, 738, 747, 756, 765, 774, 783, 792, 819, 828, 837, 846, 855, 864, 873, 882, 891, 909

Offset: 1

Amarnath Murthy, May 03 2001

			288 is a term as the arithmetic mean of the digits is (2+8+8)/3 = 6.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A061383, A061384, A061385, A061386, A061387, A061388, A061424, A061425.

[n: n in [1..1000] | &+Intseq(n) eq 6*#Intseq(n)]; // Vincenzo Librandi, Jan 28 2016

F:= proc(m,s)
option remember;
# list of all m-digit numbers with sum of digits s
if s > 9*m or s < 0 then return [] fi;
if m = 1 then return [s] fi;
[seq(seq(op(map(`+`,procname(j,s-i),10^(m-1)*i)),j=1..m-1),i=1..min(9,s))]
end proc:
seq(op(F(m,6*m)),m=1..3); # Robert Israel, Jan 27 2016

Select[Range[1000],Total[IntegerDigits[#]]==6*IntegerLength[#]&] (* Harvey P. Dale, Dec 20 2014 *)

isok(n) = {digs = digits(n, 10); return(6*#digs == sum(k=1, #digs, digs[k]));} \\ Michel Marcus, Jul 31 2013

More terms from Larry Reeves (larryr(AT)acm.org), May 16 2001

A061385 Numbers n such that sum of digits = twice number of digits.

Original entry on oeis.org

2, 13, 22, 31, 40, 105, 114, 123, 132, 141, 150, 204, 213, 222, 231, 240, 303, 312, 321, 330, 402, 411, 420, 501, 510, 600, 1007, 1016, 1025, 1034, 1043, 1052, 1061, 1070, 1106, 1115, 1124, 1133, 1142, 1151, 1160, 1205, 1214, 1223, 1232, 1241, 1250, 1304

Offset: 1

Amarnath Murthy, May 03 2001

			141 is a term as the arithmetic mean of the digits is (1+4+1)/3 = 2.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A061383, A061384, A061386, A061387, A061388, A061423, A061424, A061425.

[ n: n in [1..1310] | &+Intseq(n) eq 2*#Intseq(n) ];  // Bruno Berselli, Jun 30 2011

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(S(d,2*d,1)),d=1..5); # Robert Israel, Apr 23 2017

More terms from Larry Reeves (larryr(AT)acm.org), May 16 2001

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 *)

A268620 Numbers whose digital sum is a multiple of 4.

Original entry on oeis.org

0, 4, 8, 13, 17, 22, 26, 31, 35, 39, 40, 44, 48, 53, 57, 62, 66, 71, 75, 79, 80, 84, 88, 93, 97, 103, 107, 112, 116, 121, 125, 129, 130, 134, 138, 143, 147, 152, 156, 161, 165, 169, 170, 174, 178, 183, 187, 192, 196, 202, 206, 211, 215, 219, 220, 224, 228, 233, 237, 242, 246

Offset: 1

Bruno Berselli, Feb 09 2016

a(1498) = 5999 is the smallest term that is congruent to 5 modulo 9.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A007953, A061383 (supersequence).
Cf. numbers whose digital sum is a multiple of k: A054683 (k=2), A008585 (k=3), this sequence (k=4), A227793 (k=5).
Subsequences: A002278, A038446, A052218, A052222, A061387, A169967, A235151, A235227, A235229.

[n: n in [0..250] | IsIntegral(&+Intseq(n)/4)];

select(t -> convert(convert(t,base,10),`+`) mod 4 = 0, [$1..1000]); # Robert Israel, Feb 09 2016

Select[Range[0, 250], IntegerQ[Total[IntegerDigits[#]]/4] &]

A285093 Corresponding values of arithmetic means of digits of numbers from A061383.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 2, 3, 4, 5, 6, 2, 3, 4, 5, 6, 3, 4, 5, 6, 7, 3, 4, 5, 6, 7, 4, 5, 6, 7, 8, 4, 5, 6, 7, 8, 5, 6, 7, 8, 9, 1, 2, 3, 1, 2, 3, 1, 2, 3, 4, 2, 3, 4, 2, 3, 4, 2, 3, 4, 5, 3, 4, 5, 3, 4, 5, 3, 4, 5, 6, 4, 5, 6

Offset: 0

Jaroslav Krizek, Apr 14 2017

Jaroslav Krizek, Table of n, a(n) for n = 0..3000

Cf. A061383 (numbers with integer arithmetic mean of digits in base 10).
Sequences of numbers n such that a(n) = k for k = 1 - 9: A061384 (k = 1), A061385 (k = 2), A061386 (k = 3), A061387 (k = 4), A061388 (k = 5), A061423 (k = 6), A061424 (k = 7), A061425 (k = 8), A002283 (k = 9).
Cf. A004426, A004427, A257295 (supersequences).

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

lista(nn) = {for (n=0, nn, if (n, d = digits(n), d = [0]); if (!( vecsum(d) % #d), print1(vecsum(d)/#d, ", ")););} \\ Michel Marcus, Apr 15 2017

a(n) = A007953(A061383(n)) / A055642(A061383(n)) for n >= 1.

A316561 Squarefree numbers whose arithmetic mean of digits is 4.

Original entry on oeis.org

17, 26, 35, 53, 62, 71, 129, 138, 165, 174, 183, 219, 237, 246, 255, 273, 282, 291, 309, 318, 327, 345, 354, 381, 390, 417, 426, 435, 453, 462, 471, 534, 543, 561, 570, 606, 615, 633, 642, 651, 705, 714, 723, 741, 813, 822, 831, 903, 921, 930, 1069, 1087, 1159

Offset: 1

K. D. Bajpai, Jul 06 2018

			26 = 2*13 is a 2-digit squarefree number whose arithmetic mean of digits is (2 + 6)/2 = 4. Hence, 26 is a term.
165 = 3 * 5 * 11 is a 3-digit squarefree number whose arithmetic mean of digits is (1 + 6 + 5)/3 = 4. Hence, 165 is a term.

Robert Israel, Table of n, a(n) for n = 1..10000

Intersection of A005117 (squarefree numbers) and A061387.

Cf. A316484.

[k:k in [4..1200]| IsSquarefree(k) and &+Intseq(k) eq 4*#Intseq(k)]; // Marius A. Burtea, Dec 19 2019

filter:= proc(n) local L;
  if not numtheory:-issqrfree(n) then return false fi;
  L:= convert(n,base,10);
  convert(L,`+`)=4*nops(L)
end proc:
select(filter, [$1..1000]); # Robert Israel, Jul 06 2018

Select[Range[5000], Mean[IntegerDigits[#]] == 4 && SquareFreeQ[#] &]

cp's OEIS Frontend

A061388 Sum of digits = 5 times number of digits.

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A061423 Sum of digits = 6 times number of digits.

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A061385 Numbers n such that sum of digits = twice number of digits.

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

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A268620 Numbers whose digital sum is a multiple of 4.

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A285093 Corresponding values of arithmetic means of digits of numbers from A061383.

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A316561 Squarefree numbers whose arithmetic mean of digits is 4.

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