A076068 Smallest number that can be formed by using the nonzero digits of the numbers 1+n(n-1)/2 through n(n+1)/2.

1, 23, 456, 1789, 1111112345, 11111226789, 22222222345678, 122333333334569, 12333344444445789, 1234444455555556789, 123455555666666666789, 12345666677777777777889, 112345677888888888889999, 111111122334455678999999999, 111111111111111111111111112234566778899

Offset: 1

Author

Amarnath Murthy, Oct 05 2002

Keywords

• base
• easy
• nonn

Comments

Is there any r and s such that a(r) = a(s)? Probably not.

Examples

			a(4) = 1789 (=01789) formed by using digits of 7,8,9 and 10.
		

Crossrefs

Cf. A053067 (next n concatenated), A080479 (smallest with zeros), A080480 (largest with zeros).

Programs

Mathematica

sncbf[n_]:=Sort[Flatten[IntegerDigits/@Range[(n(n-1))/2+1,(n(n+1))/2]]/.(0->Nothing)]//FromDigits; Array[sncbf,15] (* Harvey P. Dale, Nov 26 2019 *)

Python

def a(n):
  s = "".join(sorted("".join(map(str, range((n-1)*n//2+1, n*(n+1)//2+1)))))
  if '0' not in s: return int(s)
  return int(s[s.rfind('0')+1:])
print([a(n) for n in range(1, 16)]) # Michael S. Branicky, Jan 23 2021

Extensions

More terms from David Wasserman, Mar 19 2005