A344570 Number of pairs of n-digit squares such that the final (n-1) digits of the first square coincide with the initial (n-1) digits of the second.
0, 4, 6, 7, 10, 5, 10, 4, 15, 0, 13, 5, 16, 3, 57, 2, 8, 2, 5, 1, 119, 1, 13, 8, 39, 5, 55, 2, 53, 7, 12, 7, 76, 1, 193, 2, 21, 2, 59, 11, 35, 15, 42, 7, 541, 7, 17, 20, 37, 1, 233, 3, 32, 2, 373, 19, 65, 0, 15, 16, 181, 15, 8637, 5, 175, 15
Offset: 1
Examples
For n=2: (81,16), (16,64), (36,64), (64,49). For n=3: (144,441), (196,961), (225,256), (625,256), (484,841), (784,841). For n=4: (3136,1369), (4624,6241), (5184,1849), (5476,4761), (7396,3969), (7921,9216), (9409,4096). For n=20: (64764644930975528100, 47646449309755281001) is the only pair. - _Andrew Howroyd_, May 23 2021
Links
- Stowarzyszenie na rzecz Edukacji Matematycznej, Olimpiada Matematyczna Juniorów 2020/2021, etap 1 (in Polish).
- Chai Wah Wu, pairs of squares for n = 1..46
- Index to sequences related to Olympiads.
Crossrefs
Cf. A343855.
Programs
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PARI
a(n)={sum(k=sqrtint(10^(n-1))+1, sqrtint(10^n-1), my(t=k^2*10%10^n); t>=10^(n-1) && sqrtint(t+9)^2\10==t\10)} \\ Andrew Howroyd, May 24 2021
Extensions
a(10)-a(20) from Andrew Howroyd, May 24 2021
a(21)-a(46) from Chai Wah Wu, May 26 2021
a(47)-a(66) from Chai Wah Wu, Jun 02 2021
Comments