A071648 -id:A071648 - cp's OEIS frontend

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.

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

A071650 Difference between sums of odd and even digits of n.

Original entry on oeis.org

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

Offset: 1

Reinhard Zumkeller, May 28 2002

Michel Marcus, Table of n, a(n) for n = 1..10000

Cf. A036301, A071648, A071649.

Table[Total[Select[IntegerDigits[n],OddQ]]-Total[Select[ IntegerDigits[ n],EvenQ]],{n,80}] (* Harvey P. Dale, Jul 27 2020 *)

a(n) = {my(d=digits(n), s = 0); for (k=1, #d, if (d[k] % 2, s += d[k], s -= d[k]);); s;} \\ Michel Marcus, Aug 05 2017

A071650(n)=-vecsum(apply(t->(-1)^t*t,digits(n))) \\ M. F. Hasler, Dec 09 2018

a(n) = A071649(n) - A071648(n);

a(A036301(n)) = 0.

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

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).

A341012 The cumulative sum of the even digits so far in the sequence and the cumulative sum of the odd digits so far differ by n for all a(n)s.

Original entry on oeis.org

1, 10, 16, 7, 23, 32, 45, 54, 67, 76, 89, 98, 100, 203, 225, 230, 247, 252, 269, 274, 296, 302, 320, 405, 427, 449, 450, 472, 494, 504, 522, 540, 607, 629, 670, 692, 706, 724, 742, 760, 809, 890, 908, 926, 944, 962, 980, 1000, 1112, 1121, 1134, 1143, 1156, 1165, 1178

Offset: 1

Eric Angelini and Carole Dubois, Feb 02 2021

This is the lexicographically earliest sequence of distinct integers > 0 having this property.

			Say that the current sequence is S, the cumulative sum at any moment of the even digits of S is E, the cumulative sum at any moment of the odd digits of S is O and the absolute difference |E-O| is D. We would then have:
S = 1, 10, 16, 7, 23, 32, 45, 54, 67, 76, 89, 98,...
E = 0   0   6  6   8  10  14  18  24  30  38  46
O = 1   2   3 10  13  16  21  26  33  40  49  58
D = 1   2   3  4   5   6   7   8   9  10  11  12 <-- this is = n.

Carole Dubois, Table of n, a(n) for n = 1..5000

Cf. A071648, A071649.

Cf. A341002 (numbers whose sum of even digits and sum of odd digits differ by 1).

A156614 a(1)=2, a(n+1) is the smallest prime with sum of even digits >= sum of even digits of a(n).

Original entry on oeis.org

2, 23, 29, 41, 43, 47, 61, 67, 83, 89, 181, 263, 269, 281, 283, 461, 463, 467, 487, 661, 683, 863, 881, 883, 887, 1889, 2683, 2687, 2689, 2861, 2887, 4861, 4889, 6689, 6863, 6869, 6883, 8681, 8689, 8861, 8863, 8867, 8887, 26881

Offset: 1

Juri-Stepan Gerasimov, Feb 11 2009

An increasing sequence of primes a(n) such that the sequence A071648(a(n)) is nondecreasing. - R. J. Mathar, May 15 2010

			2, 23(2=2), 29(2=2), 41(4>2), 43(4=4), 61(6>4), 67(6=6), 83(8>6), 89(8=8), 181(8=8), 263(2+6=8), 269(2+6=2+6), 281(2+8>2+6), 283(2+8=2+8), 461(4+6=2+8), etc.

Harvey P. Dale, Table of n, a(n) for n = 1..100

Cf. A000040.

t={}; max=0; Do[p=Prime[i]; If[(x=Total[Select[IntegerDigits[p],EvenQ[#] &]])>=max, max = x; AppendTo[t,p]],{i,3000}]; t (* Jayanta Basu, May 22 2013 *)
sped[p_]:=Module[{d1=Total[Select[IntegerDigits[p],EvenQ]],p2=NextPrime[p]},While[ Total[ Select[ IntegerDigits[ p2],EvenQ]]Harvey P. Dale, Jan 22 2024 *)

Corrected (4861 inserted) by R. J. Mathar, May 15 2010

cp's OEIS Frontend

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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A071650 Difference between sums of odd and even digits of n.

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A071649 Sum of odd 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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A341012 The cumulative sum of the even digits so far in the sequence and the cumulative sum of the odd digits so far differ by n for all a(n)s.

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A156614 a(1)=2, a(n+1) is the smallest prime with sum of even digits >= sum of even digits of a(n).

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