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Search: id:A136346
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| A136346 |
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Octagonal numbers which are the sums of exactly two positive octagonal numbers. |
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+0
2
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| 560, 736, 1541, 3201, 5461, 6816, 7400, 9976, 11041, 11408, 13333, 14981, 15408, 15841, 19521, 21000, 21505, 25761, 28616, 30401, 41536, 45141, 50440, 51221, 52008, 54405, 56856, 61920, 63656, 65416, 69008, 75525, 76480, 81345, 82336, 85345, 87381, 89441
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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For sums of two positive octagonal numbers, see: A136345. This is to octagonal numbers A000567 as A089982 is to triangular numbers A000217 and as A009000 is to squares A000290 and as A136117 are to pentagonal numbers A000326) and as A133215 is to hexagonal numbers A000384 and as A117104 is to heptagonal numbers A000566. If Oc(a) + Oc(b) = Oc(c) then a(3a-2) + b(3b+2) = c(3c+2), so solving the quadrataic equations for c we have (when an integer): c = (2 + SQRT(4 + 36a^2 + 36b^2 - 24a - 24b))/6.
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LINKS
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B. D. Swan, Table of n, a(n) for n=0,...,1800
Eric Weisstein's World of Mathematics, Octagonal Number
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FORMULA
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A000567 INTERSECTION {A000567(i) + A000567(j), i, j > 0}. {i*(3*i-2)} INTERSECTION {i*(3*i-2) + j(3*j-2), i > 0}.
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EXAMPLE
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Where Oc(n) = A000567(n) = n-th octagonal number:
a(1) = 560 = Oc(14) = 280 + 280 = Oc(10) + Oc(10).
a(2) = 736 = Oc(16) = 560 + 176 = Oc(14) + Oc(8).
a(3) = 1541 = Oc(23) = 1408 + 133 = Oc(22) + Oc(7).
a(4) = 3201 = Oc(33) = 2465 + 736 = Oc(29) + Oc(16).
a(5) = 5461 = Oc(43) = 2821 + 2640 = Oc(31) + Oc(30).
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CROSSREFS
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Cf. A000567, A009000, A089982, A136117, A136345.
Sequence in context: A071393 A050254 A139197 this_sequence A100987 A100971 A069243
Adjacent sequences: A136343 A136344 A136345 this_sequence A136347 A136348 A136349
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Dec 25 2007
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EXTENSIONS
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Corrected and edited by B. D. Swan (bdswan(AT)gmail.com), Dec 20 2008
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