A117104 -id:A117104 - cp's OEIS frontend

A136346 Octagonal numbers which are the sums of exactly two positive octagonal numbers.

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

Offset: 1

Jonathan Vos Post, Dec 25 2007

For sums of two positive octagonal numbers, see A136345. This is to octagonal numbers A000567 as A089982 is to triangular numbers A000217, as A009000 is to squares A000290, as A136117 is to pentagonal numbers A000326, 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 quadratic equations for c we have (when an integer): c = (2 + sqrt(4 + 36a^2 + 36b^2 - 24a - 24b))/6.

			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).

B. D. Swan, Table of n, a(n) for n = 1..1800
Eric Weisstein's World of Mathematics, Octagonal Number

Cf. A000567, A009000, A089982, A136117, A136345.

Module[{nn=300,ono},ono=PolygonalNumber[8,Range[nn]];Union[Select[ Total/@ Tuples[ono,2],MemberQ[ono,#]&]]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 26 2019 *)

A000567 INTERSECTION {A000567(i) + A000567(j), i, j > 0}. {i*(3*i-2)} INTERSECTION {i*(3*i-2) + j(3*j-2), i > 0}.

Corrected and edited by B. D. Swan (bdswan(AT)gmail.com), Dec 20 2008

A136345 Sums of exactly two positive octagonal numbers A000567.

Original entry on oeis.org

2, 9, 16, 22, 29, 41, 42, 48, 61, 66, 73, 80, 86, 97, 104, 105, 117, 130, 134, 136, 141, 154, 161, 173, 177, 184, 192, 197, 198, 216, 226, 229, 233, 241, 246, 265, 266, 272, 281, 288, 290, 301, 309, 320, 321, 342, 345, 349, 352, 358, 362, 376, 381, 401, 406, 409

Offset: 1

Jonathan Vos Post, Dec 25 2007

For octagonal numbers within this sequence, see: A136346. This is to octagonal numbers A000567 as A051533 is to triangular numbers A000217 and as A000404 is to squares A000290 and as A117104 is to heptagonal numbers A000566.

Eric Weisstein's World of Mathematics, Octagonal Number.

Cf. A000567, A136117, A136346.

{A000567(i) + A000567(j), i, j > 0}. {i*(3*i-2) + j(3*j-2), i, j > 0}.

Missing term (80) from Giovanni Resta, Jun 19 2016

cp's OEIS Frontend

A136346 Octagonal numbers which are the sums of exactly two positive octagonal numbers.

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