The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A133759 Numbers that are the sum of a nonzero pentagonal number and a nonzero square in at least one way. 0
 2, 5, 6, 9, 10, 13, 14, 16, 17, 21, 23, 26, 28, 30, 31, 36, 37, 38, 39, 41, 44, 47, 48, 50, 51, 52, 54, 55, 58, 60, 61, 65, 67, 69, 71, 74, 76, 79, 82, 84, 86, 87, 93, 95, 96, 99, 100, 101, 103, 105, 106, 108, 112, 115, 116, 117, 118, 119, 121, 122, 126, 128, 132, 133, 134 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS These pentagonal numbers P(k) that can be represented as the sum of P(i)+j^2, i,j>0, are at k= 2, 6, 9, 10, 13, 17, 21, 22, 24, 26, 29, 34, 35, 38, 41, 45, 46, 53. Are almost all positive integers in this sequence and, if so, what is the largest value in the complement? The largest square in the complement? The largest pentagonal number in the complement? LINKS FORMULA {A000326(i) + A000290(j) for i, j > 0}. {i(3*i-1)/2 + j^2 for i, j > 0}. EXAMPLE Let P(n) = n-th pentagonal number: a(1) = P(1) + 1^2 = 1 + 1 = 2. a(2) = P(1) + 2^2 = 1 + 4 = 5 = P(2). a(3) = P(2) + 1^2 = 5 + 1 = 6. a(4) = P(2) + 2^2 = 5 + 4 = 9 = 3^2. a(5) = P(1) + 3^2 = 1 + 9 = 10 = a(P(2)). a(8) = P(3) + 2^2 = 12 + 4 = 16 = 4^2. a(10) = P(2) + 4^2 = 5 + 16 = P(3) + 3^2 = 12 + 9 = 21. a(12) = P(1) + 5^2 = 1 + 25 = P(4) + 2^2 = 22 + 4 = 26 = a(P(3)). a(16) = P(5) + 1^2 = 35 + 1 = 36 = 6^2. a(17) = P(1) + 6^2 = 1 + 36 = P(3) + 5^2 = 12 + 25 = 37. a(25) = P(5) + 4^2 = 35 + 16 = 51 = P(6). a(30) = P(6) + 3^2 = 51 + 9 = P(5) + 5^2 = 35 + 25 = 60. a(35) = P(7) + 1^2 = 70 + 1 = P(5) + 6^2 = 35 + 36 = P(4) + 7^2 = 22 + 49 = 71 = a(P(5)). a(37) = P(6) + 5^2 = 51 + 25 = P(3) + 8^2 = 12 + 64 = 76. a(41) = P(7) + 4^2 = 70 + 16 = P(4) + 8^2 = 22 + 64 = 86. CROSSREFS Cf. A000290, A000326, A134935-A134938. Sequence in context: A031461 A085183 A340289 * A188258 A308395 A227149 Adjacent sequences:  A133756 A133757 A133758 * A133760 A133761 A133762 KEYWORD easy,nonn AUTHOR Jonathan Vos Post, Jan 21 2008 EXTENSIONS Corrected and extended by R. J. Mathar, Jan 21 2008 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 12 09:24 EDT 2021. Contains 344946 sequences. (Running on oeis4.)