A371032 - OEIS

A371032

a(n) is the integer whose decimal digits are 0's or 1's in alternating runs of lengths n, n-1, n-2, ..., 3, 2, 1.

1, 110, 111001, 1111000110, 111110000111001, 111111000001111000110, 1111111000000111110000111001, 111111110000000111111000001111000110, 111111111000000001111111000000111110000111001, 1111111111000000000111111110000000111111000001111000110

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..10.

FORMULA

a(n) = A007088(A371033(n)). - Michel Marcus, Jul 09 2024

a(n) = (10^(n*(n+1)/2) - 1)/9 - a(n-1). - Robert Israel, Jul 09 2024

EXAMPLE

a(1) = 1 has runlength 1; a(2) = 110 has runlengths 2,1; a(3) = 111001 has runlengths 3,2,1.

MAPLE

f:= proc(n) option remember; (10^(n*(n+1)/2)-1)/9 - procname(n-1) end proc:

f(1):= 1:

map(f, [$1..30]); # Robert Israel, Jul 09 2024

MATHEMATICA

Flatten[Table[Flatten[Map[ConstantArray[Mod[#, 2], n + 1 - #] &, Range[n]]], {n, 10}]] (* Peter J. C. Moses, Mar 08 2024 *)

PROG

(Python)

def A371032(n):

c = 0

for i in range(n):

c = (m:=10**(n-i))*c

if i&1^1:

c += (m-1)//9

return c # Chai Wah Wu, Mar 18 2024

CROSSREFS

Cf. A000217 (binary lengths), A007088, A065447, A371033 (decimal version).

Sequence in context: A329338 A203718 A143750 * A192844 A234512 A343181

Adjacent sequences: A371029 A371030 A371031 * A371033 A371034 A371035

KEYWORD

nonn,base,easy

AUTHOR

Clark Kimberling, Mar 09 2024

EXTENSIONS

New name from Michel Marcus, Jul 09 2024

STATUS

approved