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A238237 Numbers which when chopped into two parts with equal length, added and squared result in the same number. 8
81, 2025, 3025, 9801, 494209, 998001, 24502500, 25502500, 52881984, 60481729, 99980001, 6049417284, 6832014336, 9048004641, 9999800001, 101558217124, 108878221089, 123448227904, 127194229449, 152344237969, 213018248521, 217930248900, 249500250000, 250500250000 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 3 20:11 EDT 2022. Contains 355058 sequences. (Running on oeis4.)