A079790 a(n) = number of m <= n which can be obtained by deleting digits from n.

1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 4, 5, 6, 6, 6, 6

Offset

1,10

Comments

a(n) = A120004(n) for n <= 100. a(101) = #{0, 1, 10, 11, 101} = 5; a(102) = #{0, 1, 2, 10, 12, 102} = 6. - Reinhard Zumkeller, Jun 15 2006

From David A. Corneth, Jul 03 2026: (Start)

For some families of numbers we may have direct formulae.

For example for m in A009993 we have a(m) = 2^k - 1 where k is the number of digits of m.

For repunits m we have a(m) = k where k is the number of digits of m.

For numbers m of the form ABABAB... where A,B > 0 distinct, seem to have a(m) = Fibonacci(k+3) - 2 where k is the number of digits of m.

(End)

Links

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

Example

a(124)=7 and the numbers are 1,2,4,12,14,24,124.

Maple

f:= proc(n) local L, V;
  L:= convert(n, base, 10);
  V:= convert(map(t -> L[t], combinat:-powerset([$1..nops(L)])), set) minus {[]};
  V:= map(proc(t) local i; add(t[i]*10^(i-1), i=1..nops(t)) end proc, V);
  nops(select(t -> t <= n, V))
end proc:
map(f, [$1..100]); # Robert Israel, Dec 03 2024

Crossrefs

Cf. A009993, A039994, A120004.

Sequence in context: A080428 A343886 A120004 * A098726 A065801 A265705

Adjacent sequences: A079787 A079788 A079789 * A079791 A079792 A079793

Keyword

nonn,easy,base,changed

Author

Amarnath Murthy, Feb 04 2003

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 19 2003

Corrected and extended by Reinhard Zumkeller, Jun 15 2006

Status

approved