A062273 a(n) is an n-digit number with digits in increasing order with 0 following 9 and this is maintained in the concatenation of any number of consecutive terms.

1, 23, 456, 7890, 12345, 678901, 2345678, 90123456, 789012345, 6789012345, 67890123456, 789012345678, 9012345678901, 23456789012345, 678901234567890, 1234567890123456, 78901234567890123, 456789012345678901, 2345678901234567890, 12345678901234567890

Offset

1,2

Comments

a(n) is congruent to A000217(n), mod 10; i.e., the last digit of a(n) is the same as the last digit of the n-th triangular number, base 10 (A008954). - Carl R. White, Oct 21 2009

Links

Robert Israel, Table of n, a(n) for n = 1..999

Formula

From Carl R. White, Oct 21 2009: (Start)

a(n) = floor( 10^(10*ceiling(n/10) + (n*(n+1)/2 mod 10)) * 1234567890/9999999999 ) mod 10^n.

The generalized form g, for any integer base b (>2), is: g(b,n) = floor( b^(b*ceiling(n/b) + (n*(n+1)/2 mod b)) * floor( b^(b+1)/(b-1)^2 - (b+1) ) / (b^b-1)) mod b^n, so here a(n) = g(10,n). (End)

a(n) = Sum_{i=1..n} ((n*(n-1)/2+i) mod 10)*10^(n-i). - Vedran Glisic, Apr 08 2011

Example

a(5) = 12345 as a(4) is 7890.

Maple

f:= proc(n) option remember: local d, t, k;
  d:= procname(n-1) mod 10;
  t:= 0:
  for k from 1 to n do
    d:= d+1 mod 10;
    t:= t + d*10^(n-k)
  od:
t
end proc:
f(1):= 1:
map(f, [$1..30]); # Robert Israel, Apr 02 2018

Mathematica

FromDigits/@Table[Take[PadRight[{}, 250, Join[Range[9], {0}]], {(n(n+1))/2+ 1, ((n+1)(n+2))/2}], {n, 0, 20}] (* Harvey P. Dale, May 15 2015 *)

Prog

(PARI) a(n) = sum(i=1, n, ((n*(n-1)/2+i) % 10)*10^(n-i)); \\ Michel Marcus, May 26 2022
(Python)
def a(n): return sum((n*(n-1)//2+i)%10*10**(n-i) for i in range(1, n+1))
print([a(n) for n in range(1, 21)]) # Michael S. Branicky, May 26 2022 after Michel Marcus

Crossrefs

Cf. A000217, A008954.

Sequence in context: A174262 A174425 A076068 * A066547 A001369 A007923

Adjacent sequences: A062270 A062271 A062272 * A062274 A062275 A062276

Keyword

nonn,base,easy

Author

Amarnath Murthy, Jun 17 2001

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Jun 18 2001

Status

approved