A036301 -id:A036301 - cp's OEIS frontend

A076165 Numbers n such that sum of cubes of even digits of n equals sum of cubes of odd digits of n.

14467, 14476, 14647, 14674, 14746, 14764, 16447, 16474, 16744, 17446, 17464, 17644, 41467, 41476, 41647, 41674, 41746, 41764, 44167, 44176, 44617, 44671, 44716, 44761, 46147, 46174, 46417, 46471, 46714, 46741, 47146, 47164, 47416

Offset: 1

Zak Seidov, Nov 01 2002

Minimal number of digits in n is 5.

n such that sum of even digits equals sum of odd digits in A036301.

			14467 is OK because 1^3+7^3=4^3+4^3+6^3.

Marius A. Burtea, Table of n, a(n) for n = 1..5880

Cf. A036301, A076166.

oeQ[n_]:=Module[{idn = IntegerDigits[n]},Total[Select[idn, OddQ]^3] == Total[Select[idn, EvenQ]^3]]; Select[Range[100000],oeQ] (* Harvey P. Dale, Sep 23 2011 *)

ok(n)={my(v=digits(n)); sum(i=1, #v, v[i]^3*if(v[i]%2, 1, -1))==0} \\ Andrew Howroyd, Dec 10 2018

A076166 Primes p such that sum of cubes of even digits of p equals sum of cubes of odd digits of p.

Original entry on oeis.org

16447, 41467, 41647, 44617, 46147, 46471, 76441, 114451, 144511, 146407, 404167, 404671, 414607, 415141, 416407, 440761, 441607, 451411, 460147, 460417, 461407, 470461, 476041, 476401, 541141, 610447, 640741, 644107, 644701, 647401, 704461, 740461, 746041, 764041

Offset: 1

Zak Seidov, Nov 01 2002

Minimal number of digits in p is 5. n such that sum of even digits equals sum of odd digits in A036301.

To find terms of this sequence, one could look at zerofree positive integers having the criterion on sum of cubes of digits. Then permute the digits to see which are prime. Using those digits with 0 and permuting then only needs the check on primality. - David A. Corneth, Dec 11 2018

			16447 is OK because 1^3 + 7^3 = 6^3 + 4^3 + 4^3.
14467 has digits in nondecreasing order (is zerofree). Of the 60 permutations, 16447, 41467, 41647, 44617, 46147, 46471, 76441 are prime. - _David A. Corneth_, Dec 11 2018

Marius A. Burtea, Table of n, a(n) for n = 1..5869

Cf. A009994, A036301.

Subsequence of A076165.

oeQ[n_]:=Module[{idn = IntegerDigits[n]}, Total[Select[idn, OddQ]^3] == Total[ Select[idn, EvenQ]^3]]; Select[Range[100000], PrimeQ[#] && oeQ[#] &] (* Amiram Eldar, Dec 10 2018 after Harvey P. Dale at A076165 *)

isok(p) = isprime(p) && (d=digits(p)) && (sum(i=1, #d, d[i]^3*if(d[i]%2, 1, -1))==0); \\ Michel Marcus, Dec 13 2018

A076167 Primes p such that sum of even digits of p equals sum of odd digits of p.

Original entry on oeis.org

211, 431, 853, 1021, 1087, 1201, 1223, 1289, 1447, 1627, 2011, 2213, 2617, 2671, 2819, 2837, 3041, 3221, 3467, 4013, 4637, 4673, 4691, 5443, 5623, 5689, 5869, 6217, 6271, 6473, 6491, 7283, 7621, 7643, 7687, 7823, 7867, 8017, 8053, 8219, 8237, 8273

Offset: 1

Zak Seidov, Nov 01 2002

Primes in A036301.

			2671 is OK because 2+6=7+1.

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

Intersection of A000040 and A036301,

Cf. A111309.

f:= proc(n) local Lo,Le;
  Lo,Le:= selectremove(type,convert(n,base,10),odd);
  abs(convert(Lo,`+`)-convert(Le,`+`))
end proc:
select(t -> f(t) = 0, [seq(ithprime(i),i=1..10000)]); # Robert Israel, Nov 13 2024

soeQ[n_]:=2*Total[Select[(x=IntegerDigits[n]),OddQ[#]&]]==Total[x]; Select[Prime[Range[1050]],soeQ[#]&] (* Jayanta Basu, May 23 2013 *)
Cases[{Total@# &/@GatherBy[IntegerDigits@#,OddQ], #}&/@
Prime@Range@3000, {{x_, x_}, y_} :> y] (* Hans Rudolf Widmer, Jul 26 2024 *)

A103829 Sum of even digits less than sum of odd digits.

Original entry on oeis.org

0, 2, 4, 6, 8, 12, 14, 16, 18, 20, 21, 22, 24, 26, 28, 34, 36, 38, 40, 41, 42, 43, 44, 46, 48, 56, 58, 60, 61, 62, 63, 64, 65, 66, 68, 78, 80, 81, 82, 83, 84, 85, 86, 87, 88, 102, 104, 106, 108, 114, 116, 118, 120, 122, 124, 126, 128, 136, 138, 140, 141, 142, 144, 146

Offset: 1

Zak Seidov, Feb 17 2005

0 is assumed as even digit: A005843, A004275, A007928. Sum of even digits equals sum of odd digits A036301.

Cf. A005843, A004275, A007928, A036301.

Select[Range[300], Plus@@Select[IntegerDigits[ # ], OddQ]

A103848 Numbers n such that sum of even digits of n is larger than sum of odd digits.

Original entry on oeis.org

1, 3, 5, 7, 9, 10, 11, 13, 15, 17, 19, 23, 25, 27, 29, 30, 31, 32, 33, 35, 37, 39, 45, 47, 49, 50, 51, 52, 53, 54, 55, 57, 59, 67, 69, 70, 71, 72, 73, 74, 75, 76, 77, 79, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 103, 105, 107, 109, 110, 111, 113, 115, 117, 119

Offset: 1

Zak Seidov, Feb 18 2005

Sum of even digits equals sum of odd digits => A036301. Sum of even digits less than sum of odd digits => A103829

Cf. A036301, A103829.

Select[Range[300], Plus@@Select[IntegerDigits[ # ], OddQ]>Plus@@Select[IntegerDigits[ # ], EvenQ]&]

Mathematica program corrected by Harvey P. Dale, Oct 10 2024

A303269 Sum of squares of odd digits minus sum of squares of even digits of n.

Original entry on oeis.org

0, 1, -4, 9, -16, 25, -36, 49, -64, 81, 1, 2, -3, 10, -15, 26, -35, 50, -63, 82, -4, -3, -8, 5, -20, 21, -40, 45, -68, 77, 9, 10, 5, 18, -7, 34, -27, 58, -55, 90, -16, -15, -20, -7, -32, 9, -52, 33, -80, 65, 25, 26, 21, 34, 9, 50, -11, 74, -39, 106, -36, -35, -40, -27

Offset: 0

M. F. Hasler, May 18 2018

Up to 10^4, resp. 10^5, there are 5824, resp. 59316, positive terms. All terms from a(1) to a(11111) are nonzero: see A076164 for indices of zeros.

Cf. A076164, A071650, A036301.

A303269(n)=-vecsum(apply(d->d^2*(-1)^d,digits(n)))

A341003 Numbers whose sum of even digits and sum of odd digits differ by 2.

Original entry on oeis.org

2, 11, 20, 101, 110, 114, 123, 132, 136, 141, 145, 154, 158, 163, 167, 176, 185, 189, 198, 200, 213, 231, 312, 316, 321, 334, 338, 343, 356, 361, 365, 378, 383, 387, 411, 415, 433, 451, 514, 518, 536, 541, 558, 563, 581, 585, 613, 617, 631, 635, 653, 671, 716, 738, 761, 783

Offset: 1

Eric Angelini and Carole Dubois, Feb 02 2021

Carole Dubois, Table of n, a(n) for n = 1..5001

Cf. A036301 (sums are equal), A341002 to A341010 (sums differ by 1 to 9).

Select[Range[1000], Abs[Plus @@ Select[(d = IntegerDigits[#]), OddQ] - Plus @@ Select[d, EvenQ]] == 2 &] (* Amiram Eldar, Feb 02 2021 *)

A341004 Numbers whose sum of even digits and sum of odd digits differ by 3.

Original entry on oeis.org

3, 14, 25, 30, 36, 41, 47, 52, 58, 63, 69, 74, 85, 96, 104, 111, 122, 140, 205, 212, 221, 227, 234, 243, 249, 250, 256, 265, 272, 278, 287, 294, 300, 306, 324, 342, 360, 401, 407, 410, 423, 429, 432, 445, 454, 467, 470, 476, 489, 492, 498, 502, 508, 520, 526, 544, 562, 580

Offset: 1

Eric Angelini and Carole Dubois, Feb 02 2021

Carole Dubois, Table of n, a(n) for n = 1..5001

Cf. A036301 (sums are equal), A341002 to A341010 (sums differ by 1 to 9).

Select[Range[1000], Abs[Plus @@ Select[(d = IntegerDigits[#]), OddQ] - Plus @@ Select[d, EvenQ]] == 3 &] (* Amiram Eldar, Feb 02 2021 *)

A341005 Numbers whose sum of even digits and sum of odd digits differ by 4.

Original entry on oeis.org

4, 13, 22, 31, 40, 103, 116, 125, 130, 138, 147, 152, 161, 169, 174, 183, 196, 202, 215, 220, 233, 251, 301, 310, 318, 323, 332, 345, 354, 367, 376, 381, 389, 398, 400, 417, 435, 453, 471, 512, 521, 534, 543, 556, 565, 578, 587, 611, 619, 637, 655, 673, 691, 714, 736, 741, 758

Offset: 1

Eric Angelini and Carole Dubois, Feb 02 2021

Carole Dubois, Table of n, a(n) for n = 1..5001

Cf. A036301 (sums are equal), A341002 to A341010 (sums differ by 1 to 9).

Cf. A071650 (difference between sum of even and sum of odd digits).

Select[Range[1000], Abs[Plus @@ Select[(d = IntegerDigits[#]), OddQ] - Plus @@ Select[d, EvenQ]] == 4 &] (* Amiram Eldar, Feb 02 2021 *)

def ok(n):
  sums = [0, 0]
  for d in str(n): sums[d in "13579"] += int(d)
  return abs(sums[0] - sums[1]) == 4
print(list(filter(ok, range(759)))) # Michael S. Branicky, Apr 13 2021

A341006 Numbers whose sum of even digits and sum of odd digits differ by 5.

Original entry on oeis.org

5, 16, 27, 38, 49, 50, 61, 72, 83, 94, 106, 113, 124, 131, 142, 160, 207, 214, 229, 236, 241, 258, 263, 270, 285, 292, 308, 311, 326, 344, 362, 380, 409, 412, 421, 434, 443, 456, 465, 478, 487, 490, 500, 528, 546, 564, 582, 601, 610, 623, 632, 645, 654, 667, 676, 689, 698, 702

Offset: 1

Eric Angelini and Carole Dubois, Feb 02 2021

Carole Dubois, Table of n, a(n) for n = 1..5001

Cf. A036301 (sums are equal), A341002 to A341010 (sums differ by 1 to 9).

Select[Range[1000], Abs[Plus @@ Select[(d = IntegerDigits[#]), OddQ] - Plus @@ Select[d, EvenQ]] == 5 &] (* Amiram Eldar, Feb 02 2021 *)

cp's OEIS Frontend

A076165 Numbers n such that sum of cubes of even digits of n equals sum of cubes of odd digits of n.

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A076166 Primes p such that sum of cubes of even digits of p equals sum of cubes of odd digits of p.

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A076167 Primes p such that sum of even digits of p equals sum of odd digits of p.

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A103829 Sum of even digits less than sum of odd digits.

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Mathematica

A103848 Numbers n such that sum of even digits of n is larger than sum of odd digits.

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Extensions

A303269 Sum of squares of odd digits minus sum of squares of even digits of n.

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PARI

A341003 Numbers whose sum of even digits and sum of odd digits differ by 2.

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Mathematica

A341004 Numbers whose sum of even digits and sum of odd digits differ by 3.

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A341005 Numbers whose sum of even digits and sum of odd digits differ by 4.

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