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 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: A213713 A031461 A085183 * A188258 A227149 A042963 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

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Last modified April 25 04:12 EDT 2019. Contains 322451 sequences. (Running on oeis4.)