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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
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
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.
For square roots see A290449.
Sequence in context: A253448 A205978 A037211 * A350870 A282861 A237376
KEYWORD
nonn,base
AUTHOR
EXTENSIONS
a(12)-a(24) from Donovan Johnson, Feb 22 2014
STATUS
approved