A238237
Numbers which when chopped into two parts with equal length, added and squared result in the same number.
Original entry on oeis.org
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
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.
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Select[Range[600000]^2, EvenQ[len=IntegerLength[#]] && # == (Mod[#,10^(len/2)] + Floor[#/10^(len/2)])^2 &] (* Stefano Spezia, Jan 01 2025 *)
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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, ", "))));
A038544
a(n) = Sum_{i=0..10^n} i^3.
Original entry on oeis.org
1, 3025, 25502500, 250500250000, 2500500025000000, 25000500002500000000, 250000500000250000000000, 2500000500000025000000000000, 25000000500000002500000000000000, 250000000500000000250000000000000000, 2500000000500000000025000000000000000000
Offset: 0
a(1) = Sum_{i=0..10} i^3 = (Sum_{i=0..10} i)^2 = 3025.
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sumcu(n) = for(x=0,n,y=10^x;z=y^2*(y+1)^2/4;(print1(z","))) \\ Cino Hilliard, Jun 18 2007
A350869
a(n) = Sum_{i=0..10^n-1} i^3.
Original entry on oeis.org
0, 2025, 24502500, 249500250000, 2499500025000000, 24999500002500000000, 249999500000250000000000, 2499999500000025000000000000, 24999999500000002500000000000000, 249999999500000000250000000000000000, 2499999999500000000025000000000000000000
Offset: 0
a(1) = Sum_{i=0..9} i^3 = (Sum_{i=0..9} i)^2 = 2025.
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a[n_] := (10^n*(10^n - 1)/2)^2; Array[a, 11, 0] (* Amiram Eldar, Jan 20 2022 *)
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a(n) = my(x=10^n-1); (x*(x+1)/2)^2; \\ Michel Marcus, Jan 22 2022
A350918
Numbers k = x.y which when split into two parts x and y of equal length, added and squared result in the same number k, '.' means concatenation, and the second part y starts with 0.
Original entry on oeis.org
9801, 998001, 99980001, 9048004641, 9999800001, 923594037444, 989444005264, 999998000001, 7901234409876544, 8434234407495744, 8934133805179209, 9999999800000001, 999999998000000001, 79012345680987654321, 82644628100826446281, 83407877440792003584, 87138706300620940900
Offset: 1
(998+001)^2 = 999^2 = 998001, as x = 998 and y = 001 starts with 0, 998001 is a term.
(30+25)^2 = 55^2 = 3025, here x = 30 but y = 25 does not start with 0, hence 3025 is not a term.
A059988 \ {0, 81} is a subsequence.
Showing 1-4 of 4 results.
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