A367362 Comma transform of the nonnegative integers.

1, 12, 23, 34, 45, 56, 67, 78, 89, 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, 17, 27, 37, 47, 57, 67, 77, 87, 98, 8, 18

Offset: 0

Author

N. J. A. Sloane, Nov 22 2023

Keywords

• nonn
• base

Comments

See A367360 for further information.

Links

• Michael S. Branicky, Table of n, a(n) for n = 0..10000
• Eric Angelini, Michael S. Branicky, Giovanni Resta, N. J. A. Sloane, and David W. Wilson, The Comma Sequence: A Simple Sequence With Bizarre Properties, arXiv:2401.14346, Youtube

Crossrefs

Cf. A000030, A010879, A166499, A367360, A367361, A368362.

Programs

Maple

a:= n-> parse(cat(""||n[-1], ""||(n+1)[1])):
seq(a(n), n=0..99);  # Alois P. Heinz, Nov 22 2023

Mathematica

FromDigits /@ Partition[Rest@ Flatten[{First[#], Last[#]} & /@ IntegerDigits[Range[0, 120]]], 2, 2] (* Michael De Vlieger, Nov 22 2023 *)

Python

from itertools import count, islice, pairwise
def S(): yield from (str(i) for i in count(0))
def agen(): yield from (int(t[-1]+u[0]) for t, u in pairwise(S()))
print(list(islice(agen(), 82))) # Michael S. Branicky, Nov 22 2023

Python

def A367362(n): return (n%10)*10+int(str(n+1)[0]) # Chai Wah Wu, Dec 22 2023

Formula

a(n) = 10 * A010879(n) + A000030(n+1). - Alois P. Heinz, Nov 22 2023