A290449 -id:A290449 - cp's OEIS frontend

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

Arkadiusz Wesolowski, Feb 20 2014

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)

			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.

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

Subsequence of A102766.
Subsequence: A350870.
Cf. A006886, A038544, A059988, A350869.
For square roots see A290449.

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

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, ", "))));

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

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

cp's OEIS Frontend

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

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