A238237 Numbers which when chopped into two parts with equal length, added and squared result in the same number.

81, 2025, 3025, 9801, 494209, 998001, 24502500, 25502500, 52881984, 60481729, 99980001, 6049417284, 6832014336, 9048004641, 9999800001, 101558217124, 108878221089, 123448227904, 127194229449, 152344237969, 213018248521, 217930248900, 249500250000, 250500250000

Offset: 1

Author

Arkadiusz Wesolowski, Feb 20 2014

Keywords

• nonn
• base

Comments

Yet another variant of the Kaprekar numbers A006886. - N. J. A. Sloane, Aug 06 2017

From Bernard Schott, Jan 21 2022: (Start)

Three subsequences:

-> {(10^m-1)^2, m >= 1} = A059988 \ {0}; see example 9801.

-> {(10^m-1)^2 * 10^(2*m) / 4, m >= 1} = A350869 \ {0}; see example 2025.

-> {(10^m+1)^2 * 10^(2*m) / 4, m >= 1} = A038544 \ {1}, see example 3025. (End)

Examples

			2025 = (20 + 25)^2, so 2025 is in the sequence.
3025 = (30 + 25)^2, so 3025 is in the sequence.
9801 = (98 + 01)^2, so 9801 is in the sequence.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..25000

Crossrefs

Subsequence of A102766.

Subsequence: A350870.

Cf. A006886, A038544, A059988, A350869.

For square roots see A290449.

Programs

Mathematica

Select[Range[600000]^2, EvenQ[len=IntegerLength[#]] && # == (Mod[#,10^(len/2)] + Floor[#/10^(len/2)])^2 &] (* Stefano Spezia, Jan 01 2025 *)

PARI

forstep(m=1, 7, 2, p=10^((m+1)/2); for(n=10^m, 10^(m+1)-1, d=lift(Mod(n, p)); if(((n-d)/p+d)^2==n, print1(n, ", "))));

Formula

a(n) = A290449(n)^2. - Bernard Schott, Jan 20 2022

Extensions

a(12)-a(24) from Donovan Johnson, Feb 22 2014