A296562 Numbers k such that k = k_b1 - k_b2, where k_b1 and k_b2 are the representation of k in two different bases b1 < 10 and b2 < 10.

5, 6, 8, 9, 10, 11, 100, 114, 119, 120, 138, 380, 384, 396, 730, 767, 1509, 4761

Offset

1,1

Comments

There are binomial(8,2) = 28 possible cases:

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Bases | Numbers

----------|--------------------

b5 - b6 | 5, 114, 119, 120

b6 - b7 | 380, 384, 396

b7 - b8 | 730, 767, 1509

b8 - b9 | 4761

b4 - b6 | 8

b5 - b7 | 5

b6 - b8 | 100, 138

b4 - b7 | 6, 9

b5 - b8 | 5

b4 - b8 | 6, 10

b5 - b9 | 5

b4 - b9 | 6, 11

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All the other 16 differences do not produce any number.

Links

Table of n, a(n) for n=1..18.

Example

138 in base 6 is 350, in base 8 is 212 and 350 - 212 = 138.
4761 in base 8 is 11231, in base 9 is 6470 and 11231 - 6470 = 4761.

Maple

# Change the value of the parameters x, y for other differences
with(numtheory): P:=proc(q, x, y) local b1, b2, b1x, b2x, k, n;
for n from 1 to q do b1:=convert(n, base, x); b2:=convert(n, base, y);
b1x:=0; for k from nops(b1) by -1 to 1 do b1x:=10*b1x+b1[k]; od;
b2x:=0; for k from nops(b2) by -1 to 1 do b2x:=10*b2x+b2[k]; od;
if b1x-b2x=n then print(n); fi; od; end: P(5000, 8, 9);

Mathematica

Select[Range[5000], Function[k, AnyTrue[Subtract @@ # & /@ Subsets[Map[FromDigits@ IntegerDigits[k, #] &, Range[2, 9]], {2}], # == k &]]] (* Michael De Vlieger, Feb 16 2018 *)

Crossrefs

Cf. A007088, A007089, A007090, A007091, A007092, A007093, A007094, A007095.

Sequence in context: A299538 A201512 A242290 * A057854 A033266 A355641

Adjacent sequences: A296559 A296560 A296561 * A296563 A296564 A296565

Keyword

nonn,base,easy,fini,full

Author

Paolo P. Lava, Feb 15 2018

Status

approved