A071650 -id:A071650 - cp's OEIS frontend

A036301 Numbers whose sum of even digits and sum of odd digits are equal.

0, 112, 121, 134, 143, 156, 165, 178, 187, 211, 314, 336, 341, 358, 363, 385, 413, 431, 516, 538, 561, 583, 615, 633, 651, 718, 781, 817, 835, 853, 871, 1012, 1021, 1034, 1043, 1056, 1065, 1078, 1087, 1102, 1120, 1201, 1210, 1223, 1232, 1245, 1254, 1267, 1276, 1289, 1298

Offset: 1

Patrick De Geest, Dec 15 1998

John Cerkan, Table of n, a(n) for n = 1..10000

Cf. A071650 (sum of odd digits minus sum of even digits).

[ n: n in [0..1300] | (#A eq 0 select 0 else &+A) eq (#B eq 0 select 0 else &+B) where A is [ d: d in D | IsOdd(d) ] where B is [ d: d in D | IsEven(d) ] where D is Intseq(n) ];

Select[Range[0,10000], Plus @@Select[IntegerDigits[ # ], OddQ]\[Equal]Plus @@Select[IntegerDigits[ # ], EvenQ]&] (* Zak Seidov, Feb 17 2005 *)

select( is_A036301(n)=!vecsum(apply(t->(-1)^t*t,digits(n))), [0..1999]) \\ This defines the function is_A036301 = !A071650; the surrounding select(...) just serves as a check and illustration. - M. F. Hasler, Dec 09 2018
A36301=[112]; A036301(n, L=#A36301)={while(n>L, A36301=concat(A36301, next_A036301(A36301[L], L, L+=1))); A36301[n]} \\ M. F. Hasler, Aug 11 2023
next_A036301(N, L=#A36301, k=setsearch(A36301, N+1, 1)) = if(k>L, until( is_A036301(N+=1),); N, k, A36301[k], N+1) \\ next larger term: min { a(k) > N }. - M. F. Hasler, Aug 11 2023

def eodiff(n):
  digs = list(map(int, str(n)))
  return abs(sum(d for d in digs if d%2==0)-sum(d for d in digs if d%2==1))
def aupto(lim): return [m for m in range(lim+1) if eodiff(m) == 0]
print(aupto(1298)) # Michael S. Branicky, Feb 21 2021

This set A036301 = { n | A071650(n) = 0 }. - M. F. Hasler, Aug 11 2023

Zero added by Zak Seidov, Nov 22 2010

Name edited by Michel Marcus, Jan 14 2021

A124176 Consider the map f that sends m to m + (sum of odd digits of m) - (sum of even digits of m). Sequence gives numbers m such that f^(k)(m) = m for some k.

Original entry on oeis.org

0, 11, 13, 17, 18, 25, 28, 54, 55, 64, 65, 112, 121, 134, 137, 143, 148, 155, 156, 165, 166, 173, 178, 184, 187, 198, 200, 209, 211, 216, 231, 233, 234, 237, 244, 245, 270, 275, 280, 285, 314, 336, 341, 358, 363, 385, 396, 402, 407, 410, 413, 429, 431, 432

Offset: 1

Eric Angelini, Dec 04 2006

Terms computed by Barry and Theunis de Jong.

Subsequence A036301 lists fixed points of the map f = A304439. - M. F. Hasler, May 18 2018

			11 and 13 loop on themselves, but 12 doesn't:
11 -> 13 -> 17 -> 25 -> 28 -> 18 -> 11
12 -> 11 -> 13 -> 17 -> 25 -> 28 -> 18 -> 11
13 -> 17 -> 25 -> 28 -> 18 -> 11 -> 13.

Eric Angelini, Dec 04 2006, Table of n, a(n) for n = 1..172

Cf. A124177, A036301, A304439; A071648, A071649, A071650.

is(n,S=List())=until(setsearch(Set(S),n=A304439(n)),listput(S,n));n==S[1] \\ M. F. Hasler, May 18 2018

A124177 Consider the map f that sends m to m + (sum of even digits of m) - (sum of odd digits of m). Sequence gives numbers m such that f^(k)(m) = m for some k.

Original entry on oeis.org

0, 22, 26, 27, 34, 35, 44, 49, 52, 63, 66, 78, 79, 81, 88, 99, 104, 107, 108, 112, 115, 121, 126, 133, 134, 143, 144, 151, 156, 165, 178, 187, 211, 224, 229, 232, 233, 283, 290, 314, 336, 341, 358, 363, 385, 413, 431, 467, 470, 489, 492, 516, 538, 561, 583, 615

Offset: 1

Eric Angelini, Dec 04 2006

Terms computed by Theunis de Jong.

Subsequence A036301 lists fixed points of the map f = A304440. - M. F. Hasler, May 18 2018

			26 and 27 loop on themselves, but 28 doesn't.
26 -> 34 -> 35 -> 27 -> 22 -> 26
27 -> 22 -> 26 -> 34 -> 35 -> 27
28 -> 38 -> 43 -> 44 -> 52 -> 49 -> 44.

Eric Angelini, Table of n, a(n) for n = 1..182
Eric Angelini, Self-loopers.

Cf. A124176, A036301, A304439, A304440, A071650, A071648, A071649.

is(n,S=List())={until(setsearch(Set(S),n=A304440(n)),listput(S,n));n==S[1]} \\ M. F. Hasler, May 18 2018

A071649 Sum of odd decimal digits of n.

Original entry on oeis.org

1, 0, 3, 0, 5, 0, 7, 0, 9, 1, 2, 1, 4, 1, 6, 1, 8, 1, 10, 0, 1, 0, 3, 0, 5, 0, 7, 0, 9, 3, 4, 3, 6, 3, 8, 3, 10, 3, 12, 0, 1, 0, 3, 0, 5, 0, 7, 0, 9, 5, 6, 5, 8, 5, 10, 5, 12, 5, 14, 0, 1, 0, 3, 0, 5, 0, 7, 0, 9, 7, 8, 7, 10, 7, 12, 7, 14, 7, 16, 0, 1, 0, 3, 0, 5, 0, 7, 0, 9, 9, 10, 9

Offset: 1

Reinhard Zumkeller, May 28 2002

a(n) = A007953(n) - A071648(n).

Cf. A014263, A071650.

A071649 := proc(n)
      local a,d;
      a := 0 ;
      for d in convert(n,base,10) do
        if type(d,'odd') then
            a := a+d ;
        end if;
    end do:
    a ;
end proc: # R. J. Mathar, Feb 02 2015

Table[Total[Select[IntegerDigits[n], OddQ[#] &]],{n,92}] (* Jayanta Basu, May 23 2013 *)

a(n)=my(d=digits(n)); sum(i=1,#d,if(d[i]%2,d[i])) \\ Charles R Greathouse IV, Apr 04 2014

A071649(n)=vecsum(select(d->bittest(d,0), digits(n))) \\ Nearly twice as fast. - M. F. Hasler, Dec 09 2018

A071649 = lambda x: sum(d for d in map(int, str(x)) if d&1) # M. F. Hasler, Dec 07 2022

a(n) = 0 iff n is in A014263. - Bernard Schott, Mar 17 2023

A071648 Sum of even decimal digits of n.

Original entry on oeis.org

0, 2, 0, 4, 0, 6, 0, 8, 0, 0, 0, 2, 0, 4, 0, 6, 0, 8, 0, 2, 2, 4, 2, 6, 2, 8, 2, 10, 2, 0, 0, 2, 0, 4, 0, 6, 0, 8, 0, 4, 4, 6, 4, 8, 4, 10, 4, 12, 4, 0, 0, 2, 0, 4, 0, 6, 0, 8, 0, 6, 6, 8, 6, 10, 6, 12, 6, 14, 6, 0, 0, 2, 0, 4, 0, 6, 0, 8, 0, 8, 8, 10, 8, 12, 8, 14, 8, 16, 8, 0, 0, 2

Offset: 1

Reinhard Zumkeller, May 28 2002

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Cf. A007953, A071649, A071650.

Array[Total@ Select[IntegerDigits@ #, EvenQ] &, 101] (* Michael De Vlieger, Dec 09 2018 *)

a(n)=my(d=digits(n)); sum(i=1,#d,if(d[i]%2,,d[i])) \\ Charles R Greathouse IV, Apr 04 2014

A071648(n)=vecsum(select(d->!bittest(d,0),digits(n))) \\ Nearly twice as fast. - M. F. Hasler, Dec 09 2018

a(n) = A007953(n) - A071649(n). (Corrected by M. F. Hasler, Dec 09 2018)

A304439 Add to n the sum of its odd digits minus the sum of its even digits.

Original entry on oeis.org

0, 2, 0, 6, 0, 10, 0, 14, 0, 18, 11, 13, 11, 17, 11, 21, 11, 25, 11, 29, 18, 20, 18, 24, 18, 28, 18, 32, 18, 36, 33, 35, 33, 39, 33, 43, 33, 47, 33, 51, 36, 38, 36, 42, 36, 46, 36, 50, 36, 54, 55, 57, 55, 61, 55, 65, 55, 69, 55, 73, 54, 56, 54, 60, 54, 64, 54, 68, 54, 72

Offset: 0

M. F. Hasler, May 18 2018

Subsequence A036301 lists fixed points of this map, the first nontrivial one being 112. It is a subsequence of A124176 (and A124177) which considers iterations of this map, more precisely, numbers which are in a cyclic orbit for iterations of this map.

Cf. A304440, A071650, A071648, A071649, A036301, A124176, A124177.

soded[n_]:=Module[{idn=IntegerDigits[n]},n+Total[Select[idn,OddQ]]-Total[ Select[idn,EvenQ]]]; Array[soded,70,0] (* Harvey P. Dale, Aug 12 2021 *)

A304439(n)=n-vecsum(apply(t->t*(-1)^t,digits(n)))

a(n) = n + A071650(n).

A304440 Add to n the sum of its even digits minus the sum of its odd digits.

Original entry on oeis.org

0, 0, 4, 0, 8, 0, 12, 0, 16, 0, 9, 9, 13, 9, 17, 9, 21, 9, 25, 9, 22, 22, 26, 22, 30, 22, 34, 22, 38, 22, 27, 27, 31, 27, 35, 27, 39, 27, 43, 27, 44, 44, 48, 44, 52, 44, 56, 44, 60, 44, 45, 45, 49, 45, 53, 45, 57, 45, 61, 45, 66, 66, 70, 66, 74, 66, 78, 66, 82, 66, 63

Offset: 0

M. F. Hasler, May 18 2018

A036301 lists fixed points of this map, the first nonzero one being 112. It is also a subsequence of A124177 (and A124176) which lists numbers which are in a cyclic orbit under iterations of this map.

Cf. A304439 (variant: + even - odd digits), A071650 (odd - even digits), A071648, A071649, A036301 (fixed points), A124177, A124176.

nseo[n_]:=Module[{idn=IntegerDigits[n]},n+Total[Select[idn,EvenQ]]-Total[Select[idn,OddQ]]]; Array[nseo,80,0] (* Harvey P. Dale, Dec 26 2023 *)

A304440(n)=n+vecsum(apply(t->t*(-1)^t,digits(n)))

a(n) = n - A071650(n).

A111309 Absolute difference between the sum of the odd digits and the sum of the even digits of the n-th prime.

Original entry on oeis.org

2, 3, 5, 7, 2, 4, 8, 10, 1, 7, 4, 10, 3, 1, 3, 8, 14, 5, 1, 8, 10, 16, 5, 1, 16, 2, 4, 8, 10, 5, 6, 5, 11, 13, 6, 7, 13, 2, 2, 11, 17, 6, 11, 13, 17, 19, 0, 1, 3, 5, 4, 10, 5, 4, 10, 5, 1, 6, 12, 9, 7, 10, 10, 5, 7, 11, 7, 13, 6, 8, 11, 17, 4, 13, 19, 2, 4, 19, 3, 5, 6, 5, 0, 2, 8, 5, 1, 8, 9, 7, 3

Offset: 1

Zak Seidov and Robert G. Wilson v, Mar 02 2005

			a(9)=1 because the 9th prime is 23 and the absolute difference between 2 & 3 is 1.

Robert Israel, Table of n, a(n) for n = 1..10000
Ivars Peterson, Light Rings

Cf. A071650, A076167.

f:= proc(n) local Lo,Le;
  Lo,Le:= selectremove(type,convert(n,base,10),odd);
  abs(convert(Lo,`+`)-convert(Le,`+`))
end proc:
map(f, [seq(ithprime(i),i=1..100)]); # Robert Israel, Nov 12 2024

f[n_] := (id = IntegerDigits[ Prime[n]]; Abs[(Plus @@ id) - 2Plus @@ Select[id, OddQ]]); Table[f[n], {n, 91}]

Edited by Charles R Greathouse IV, Aug 04 2010

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)))

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

cp's OEIS Frontend

A036301 Numbers whose sum of even digits and sum of odd digits are equal.

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A124176 Consider the map f that sends m to m + (sum of odd digits of m) - (sum of even digits of m). Sequence gives numbers m such that f^(k)(m) = m for some k.

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A124177 Consider the map f that sends m to m + (sum of even digits of m) - (sum of odd digits of m). Sequence gives numbers m such that f^(k)(m) = m for some k.

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A071649 Sum of odd decimal digits of n.

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A071648 Sum of even decimal digits of n.

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A304439 Add to n the sum of its odd digits minus the sum of its even digits.

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A304440 Add to n the sum of its even digits minus the sum of its odd digits.

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A111309 Absolute difference between the sum of the odd digits and the sum of the even digits of the n-th prime.

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