A290148 a(n) is the integer resulting from the concatenation of the unit digit of n-1 to the digits of n without its own unit digit.

0, 1, 2, 3, 4, 5, 6, 7, 8, 91, 1, 11, 21, 31, 41, 51, 61, 71, 81, 92, 2, 12, 22, 32, 42, 52, 62, 72, 82, 93, 3, 13, 23, 33, 43, 53, 63, 73, 83, 94, 4, 14, 24, 34, 44, 54, 64, 74, 84, 95, 5, 15, 25, 35, 45, 55, 65, 75, 85, 96, 6, 16, 26, 36, 46, 56, 66, 76, 86, 97, 7

Offset: 1

Author

Michel Marcus, Jul 21 2017

Keywords

• nonn
• base
• look

Comments

Take list of integers n >= 1, move the right-most digit of each term to the start of the next term.

Every number appears, see A381225. - N. J. A. Sloane, Feb 23 2025

Examples

			For n=46, n-1 is 45, so a(46) is the concatenation of 5 (the unit digit of 45) and 4 (46 without 6), giving 54.
For n=123, n-1 is 122, so a(123) is the concatenation of 2 (the unit digit of 122) and 12 (123 without 3), giving 212.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A004216, A032762, A381225.

Programs

Maple

f:= n -> (n-1 mod 10) * 10^ilog10(n) + floor(n/10);

PARI

a(n) = my(precd = (n-1)%10); if (n < 10, precd, eval(concat(Str(precd), Str(n\10))));

Python

def a(n): return 0 if n == 1 else int(str((n-1)%10)+ str(n)[:-1])
print([a(n) for n in range(1, 72)]) # Michael S. Branicky, Feb 22 2025

Formula

a(n) = (n-1 mod 10)*10^A004216(n) + floor(n/10). # Robert Israel, Jul 21 2017