A281254 Concatenate the decimal numbers n n-2 n-4 ...5 3 1 2 4 ... n-5 n-3 n-1 if n is odd, or n n-2 n-4 ... 6 4 2 1 3 5 ... n-5 n-3 n-1 if n is even.

1, 21, 312, 4213, 53124, 642135, 7531246, 86421357, 975312468, 10864213579, 1197531246810, 121086421357911, 13119753124681012, 1412108642135791113, 151311975312468101214, 16141210864213579111315, 1715131197531246810121416

Offset: 1

Author

Robert G. Wilson v, Jan 18 2017

Keywords

• nonn
• base

Comments

The old name was "Alternately concatenate the decimal digits from back to front 1...n such that n is always to the left.".

a(40714), with 192464 decimal digits, is the sequence's first (probable) prime. - Hans Havermann, Dec 17 2019

The terms at even indices are the same as the even-indexed terms of A053063. - Hans Havermann, Jan 16 2020

Examples

			a(13) = 13119753124681012.
		

Links

• Indranil Ghosh, Table of n, a(n) for n = 1..340

Crossrefs

See A053063 for another version.

Cf. A000422, A007908, A138793, A138957, A281253.

Programs

Maple

b:= proc(n) b(n):= `if`(n=1, 1, parse(cat(a(n-1), n))) end:
a:= proc(n) a(n):= `if`(n=1, 1, parse(cat(n, b(n-1)))) end:
seq(a(n), n=1..20);  # Alois P. Heinz, Jan 18 2017

Mathematica

f[n_] := Fold[ If[ Mod[n +#2, 2] == 0, #2, #1]*10^IntegerLength@ If[ Mod[n +#2, 2] == 0, #1, #2] +If[ Mod[n +#2, 2] == 1, #2, #1] &, 0, Range@ n]; Array[f, 17]

Python

def a(n):
    if n==1:
        return ["1"]
    return [str(n)]+a(n-1)[::-1]
def A281254(n):
    return "".join(a(n)) # Indranil Ghosh, Jan 23 2017

Extensions

Edited by N. J. A. Sloane, Dec 07 2019