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

1,1

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)

Links

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

Formula

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

Example

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.

Prog

(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, ", "))));

Crossrefs

Subsequence of A102766.

Subsequence: A350870.

Cf. A006886, A038544, A059988, A350869.

For square roots see A290449.

Sequence in context: A253448 A205978 A037211 * A350870 A282861 A237376

Adjacent sequences: A238234 A238235 A238236 * A238238 A238239 A238240

Keyword

nonn,base

Author

Arkadiusz Wesolowski, Feb 20 2014

Extensions

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

Status

approved