A115549 Numbers k such that the concatenation of k with 8*k gives a square.

3, 12, 28, 63, 112, 278, 1112, 2778, 11112, 27778, 111112, 277778, 1111112, 2777778, 4938272, 7716050, 11111112, 12802888, 13151250, 13504288, 13862002, 14224392, 14591458, 14963200, 15339618, 15720712, 16106482, 16496928, 16892050, 17291848, 17696322, 18105472

Offset: 1

Author

Giovanni Resta, Jan 25 2006

Keywords

• nonn
• base

Comments

If k = 10*R_m + 2, with m >= 1, then the concatenation of k with 8*k equals (30*R_m + 6)^2, so A047855 \ {1,2} is a subsequence. - Bernard Schott, Apr 09 2022

Numbers k such that A009470(k) is a square. - Michel Marcus, Apr 09 2022

The numbers 28, 278, 2778, ..., 2*10^k + 7*(10^k - 1)/9 + 1, ..., k >= 1, are terms, because the concatenation forms the squares 28224 = 168^2, 2782224 = 1668^2, 277822224 = 16668^2, ..., (10^m + 2*(10^m - 1)/3 + 2)^2, m >= 2, ... - Marius A. Burtea, Apr 10 2022

Examples

			3_24 = 18^2.
11112_88896 = 33336^2.
		

Links

• Marius A. Burtea, Table of n, a(n) for n = 1..176

Crossrefs

Cf. A002275, A047855, A009470, A102567, A106497, A115527-A115556.

Programs

Magma

[n:n in [1..20000000]|IsSquare(Seqint(Intseq(8*n) cat Intseq(n)))]; // Marius A. Burtea, Apr 10 2022

PARI

isok(k) = issquare(eval(Str(k, 8*k))); \\ Michel Marcus, Apr 09 2022

Extensions

More terms from Marius A. Burtea, Apr 13 2022