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Search: id:A110209
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| A110209 |
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1 + sum of first n 3-almost primes. |
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3
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| 1, 9, 21, 39, 59, 86, 114, 144, 186, 230, 275, 325, 377, 440, 506, 574, 644, 719, 795, 873, 965, 1063, 1162, 1264, 1369, 1479, 1593, 1709, 1826, 1950, 2075, 2205, 2343, 2490, 2638, 2791, 2945, 3109, 3274, 3444, 3615, 3787, 3961, 4136, 4318, 4504, 4692
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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First differences are the sequence of 3-almost primes (A014612). Hence a(n) is the least positive sequence whose first differences are the sequence of 3-almost primes. Primes in this sequence include: a(1) = a(4) = 59, a(17) = 719, a(21) = 1063, a(27) = 1709, a(35) = 2791, a(37) = 3109, . Semiprimes in this sequence include: a(1) = 3^2, a(2) = 21 = 3 * 7, a(3) = 39 = 3 * 13, a(5) = 86 = 2 * 43, a(12) = 377 = 13 * 29, a(20) = 965 = 5 * 193, a(24) = 1369 = 37^2, a(34) = 2638 = 2 * 1319, a(38) = 3274 = 2 * 1637, a(41) = 3787 = 7 * 541, a(42) = 3961 = 17 * 223, a(47) = 4882 = 2 * 2441. 3-almost primes in this sequence include: a(1) = 2^3, a(6) = 114 = 2 * 3 * 19, a(8) = 186 = 2 * 3 * 31, a(9) = 230 = 2 * 5 * 23, a(10) = 275 = 5^2 * 11, a(11) = 325 = 5^2 * 13, a(14) = 506 = 2 * 11 * 23, a(15) = 574 = 2 * 7 * 41, a(18) = 795 = 3 * 5 * 53, a(19) = 873 + 3^2 * 97, a(22) = 1162 = 2 * 7 * 83, a(25) = 1479 = 3 * 17 * 29, a(28) = 1826 = 2 * 11 * 83, a(30) = 2075 = 5^2 * 83, a(32) = 2343 = 3 * 11 * 71, a(36) = 2945 = 5 * 19 * 31, a(40) = 3615 = 3 * 5 * 241, a(44) = 4318 = 2 * 17 * 127. Note also the powers a(7) = 144 = 12^2.
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FORMULA
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a(0) = 1; for n>0, a(n) = 1 + A086062(n).
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CROSSREFS
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Cf. A014612, A086062, A110208, A110226.
Sequence in context: A059993 A036704 A107890 this_sequence A053476 A110680 A020137
Adjacent sequences: A110206 A110207 A110208 this_sequence A110210 A110211 A110212
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost2(AT)yahoo.com), Sep 06 2005
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