A272617 Concatenation of the numbers from n down to 1 with numbers from 1 to n.

11, 2112, 321123, 43211234, 5432112345, 654321123456, 76543211234567, 8765432112345678, 987654321123456789, 1098765432112345678910, 11109876543211234567891011, 121110987654321123456789101112, 1312111098765432112345678910111213, 14131211109876543211234567891011121314

Offset: 1

Author

José de Jesús Camacho Medina, May 03 2016

Keywords

• nonn
• base

Comments

Conjecture: a(1) is the only prime number.

No other prime terms up to a(8000). - Giovanni Resta, May 07 2016

Examples

			a(1) = concatenate("1", "1") = 11.
a(2) = concatenate("2", "1", "1", "2") = 2112.
a(3) = concatenate("3", "2", "1", "1", "2", "3") = 321123.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A259937, A007942.

Programs

Mathematica

FromDigits@Flatten@IntegerDigits@Join[Reverse@#, #] & /@ Table[Range@n, {n, 20}]

PARI

a(n)={fromdigits(concat(concat(Vecrev(vector(n,i,digits(i)))), concat(vector(n,i,digits(i)))))} \\ Andrew Howroyd, Dec 23 2019

Formula

a(n) = A000422(n) concatenated with A007908(n).

Extensions

Terms a(11) and beyond from Andrew Howroyd, Dec 23 2019