A098129 Concatenate 1 once, 2 twice, 3 three times, up to n n times.

1, 122, 122333, 1223334444, 122333444455555, 122333444455555666666, 1223334444555556666667777777, 122333444455555666666777777788888888, 122333444455555666666777777788888888999999999

Offset: 1

Author

Michael Joseph Halm, Jan 04 2005

Keywords

• easy
• nonn
• base

Comments

a(n) is composite for all 2 <= n <= 1000. - David Cleaver, Mar 22 2023

Examples

			a(4) = 1223334444 because 1 concatenated once then concatenated with 2 twice and 3 three times and 4 four times gives 1223334444.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..31

Crossrefs

Cf. A000461, A300517, A361751 (number of decimal digits).

Programs

Maple

a:= n-> parse(cat(seq(i$i, i=1..n))):
seq(a(n), n=1..12);  # Alois P. Heinz, Mar 07 2018

Mathematica

nn = 12; a[0] = {}; Do[Set[a[n], Join[a[n - 1], Flatten@ ConstantArray[IntegerDigits[n], n]]], {n, nn}]; Array[FromDigits @* a, nn] (* Michael De Vlieger, Mar 29 2023 *)

PARI

a(n) = {my(a=0,i,k);
  for(i=1,n, k = logint(i,10)+1;
    a = a*10^(i*k) + i*(10^(i*k)-1)/(10^k-1);
); return(a); } \\ David Cleaver, Mar 29 2023

Python

def A098129(n): return int(''.join(str(j)*j for j in range(1,n+1))) # Chai Wah Wu, Mar 29 2023

Extensions

Offset and a(8) corrected by Seiichi Manyama, Mar 07 2018