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

Author

Patrick De Geest, Dec 15 1998

Keywords

• nonn
• base

Links

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

Crossrefs

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

Programs

Magma

[ 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) ];

Mathematica

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

PARI

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

Python

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

Formula

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

Extensions

Zero added by Zak Seidov, Nov 22 2010

Name edited by Michel Marcus, Jan 14 2021