A304440 -id:A304440 - cp's OEIS frontend

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.

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

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).

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

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