A304439 -id:A304439 - 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

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).

A076164 Numbers n such that sum of squares of even digits of n equals sum of squares of odd digits of n.

Original entry on oeis.org

0, 11112, 11121, 11211, 11356, 11365, 11536, 11563, 11635, 11653, 12111, 13156, 13165, 13516, 13561, 13615, 13651, 15136, 15163, 15316, 15361, 15613, 15631, 16135, 16153, 16315, 16351, 16513, 16531, 21111, 31156, 31165, 31516, 31561

Offset: 1

Zak Seidov, Nov 01 2002

The minimal number of digits in any nonzero term is 5.

Numbers such that the sum of even digits equals the sum of odd digits are listed in A036301.

			11356 is in the sequence because 1^2 + 1^2 + 3^2 + 5^2 = 6^2.

Cf. A303269, A036301 (analog without squares), A071650, A304439, A304440, A124176, A124177.

oeQ[n_]:=Module[{idn=IntegerDigits[n]},Total[Select[idn,OddQ]^2]== Total[ Select[ idn, EvenQ]^2]]; Select[Range[0,99999],oeQ] (* Harvey P. Dale, Sep 23 2011 *)

is(n)=!vecsum(apply(d->d^2*(-1)^d,digits(n))) \\ M. F. Hasler, May 18 2018

Edited and a(1) = 0 added by M. F. Hasler, May 18 2018

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

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A076164 Numbers n such that sum of squares of even digits of n equals sum of squares of odd digits of n.

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