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A055793
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Numbers n such that n and floor[n/3] are both squares; i.e. squares which remain squares when written in base 3 and last digit is removed.
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26
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0, 1, 4, 49, 676, 9409, 131044, 1825201, 25421764, 354079489, 4931691076, 68689595569, 956722646884, 13325427460801, 185599261804324, 2585064237799729, 36005300067391876, 501489136705686529, 6984842613812219524, 97286307456665386801
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Or, squares of the form 3n^2+1.
See A023110, A204503, A204515, A204517, A204519, A055812, A055808 and A055792 for the analog in other bases.
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REFERENCES
| Tom C. Brown and Peter J Shiue, Squares of second-order linear recurrence sequences, Fib. Quart., 33 (1994), 352-356.
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FORMULA
| Conjecture: a(n)=3*A098301(n-2)+1. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 11 2009]
a(n)=14*a(n-1)-a(n-2)-6, with a(0)=1,a(1)=4. (See Brown and Shiue)
a(n)=(A001075(n-2))^2. [From Johannes Boot (jgboot(AT)absamail.co.za) Dec 16 2011, Corrected by M. F. Hasler, Jan 15 2012]
G.f. = x*(1 - 11*x + 4*x^2)/((1 - x)*(1 - 14*x + x^2)). - M. F. Hasler, Jan 15 2012
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EXAMPLE
| a(3) = 49 because 49 = 7^2 = 1211 base 3 and 121 base 3 = 16 = 4^2.
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PROG
| (PARI) sq3nsqplus1(n) = { for(x=1, n, y = 3*x*x+1; \ print1(y" ") if(issquare(y), print1(y" ")) ) }
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CROSSREFS
| Cf. A023110.
Sequence in context: A199028 A189146 A086094 * A202829 A204233 A144656
Adjacent sequences: A055790 A055791 A055792 * A055794 A055795 A055796
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KEYWORD
| base,nonn
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Jul 14 2000
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EXTENSIONS
| More terms from Cino Hilliard (hillcino368(AT)gmail.com), Mar 01 2003
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