A071650 -id:A071650 - cp's OEIS frontend

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

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

A364863 Number of iterations of x -> x + min { k in A036301 | k > x } until an element of A036301 is reached, or -1 if this never happens, starting with n.

Original entry on oeis.org

0, 21

Offset: 0

M. F. Hasler, Aug 11 2023

The question whether the iteration always reaches an element of A036301 was raised on the SeqFan list in 2018, with "closest" instead of "next larger" (element of A036301). In that case one has 0 < n < 56 as a trivial counterexample. It is still open to our knowledge.

The first unknown term is currently a(2). Starting with x =2 we reach x = 336917039990529107004169 after 72 iterations.

			a(0) = 0 because n = 0 is an element of A036301 and therefore no iteration is required to reach such an element.
The smallest nonzero element of A036301 is 112. Therefore, all smaller positive numbers 0 < n < 112 go to n + 112 under the first iteration of
  f: x -> x + min { k in A036301 | k > x }.
Under iterations of f, 1 -> 113 -> 234 -> 548 -> 1109 -> 2229 -> 4460 -> 8931 -> 17865 -> 35872 -> 71875 -> 143891 -> 287898 -> 575804 -> 1151810 -> 2303826 -> 4607657 -> 9215347 -> 18430735 -> 36861480 -> 73723189 -> 147446477 which is the first element of A036301 to be reached, after a(1) = 21 iterations.

Eric Angelini, Balanced/Unbalanced numbers (and iterations), personal blog "Cinquante signes" on blogspot,com, June 23, 2023
Eric Angelini, Balanced/Unbalanced numbers (and iterations), personal blog "Cinquante signes" on blogspot,com, June 23, 2023 [Cached copy]
M. F. Hasler and N. J. A. Sloane, in reply to E. Angelini, Re: Balanced / Unbalanced numbers, Dec. 10, 2018

Cf. A036301, A071650.

a(n) = for(k=0,oo, A071650(n) || return(k); n+=next_A036301(n))

a(n) = 0 iff A071650(n) = 0, i.e., for all n in A036301.

cp's OEIS Frontend

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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