A032945 Numbers k whose base-10 representation Sum_{i=0..m} d(i)*10^(m-i) has d(i)=0 for all odd i. Here m is the position of the lead digit of k.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 400, 401, 402, 403

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• base

Comments

Every nonnegative integer can be represented as the sum of two members of this sequence. - Franklin T. Adams-Watters, Aug 30 2014

This first differs from A236402 at a(110)=1000 (followed by 1010, 1020, 1030, ...), while A236402(110)=910 (followed by 1000, 1001, 1002, ...). - M. F. Hasler, Dec 28 2014

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A126684.

Programs

Maple

N:= 6: # to get all terms with up to N digits
A[1]:= 0:
count:= 1:
for d from 1 to N do
   dp:= ceil(d/2);
   for j from 10^(dp-1) to 10^dp-1 do
      L:= ListTools[Reverse](convert(j,base,10));
      L:= ListTools[Interleave](L,[0$(d-dp)]);
      count:= count+1;
      A[count]:= add(L[i]*10^(d-i),i=1..d);
    od
od:
seq(A[i],i=1..count); # Robert Israel, Aug 31 2014

PARI

is(n)=!forstep(i=2,#n=digits(n),2,n[i]&&return) \\ M. F. Hasler, Dec 28 2014

Python

def ok(n): return str(n)[1::2].strip('0') == ""
print([k for k in range(404) if ok(k)]) # Michael S. Branicky, Apr 12 2022

Extensions

Definition corrected by Franklin T. Adams-Watters, Aug 30 2014