

A110209


1 + sum of first n 3almost primes.


2



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
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OFFSET

0,2


COMMENTS

First differences are the sequence of 3almost primes (A014612). Hence a(n) is the least positive sequence whose first differences are the sequence of 3almost 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. 3almost 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.


LINKS

Table of n, a(n) for n=0..46.


FORMULA

a(0) = 1; for n>0, a(n) = 1 + A086062(n).


CROSSREFS

Cf. A014612, A086062, A110208, A110226.
Sequence in context: A036704 A338911 A107890 * A184040 A242990 A053476
Adjacent sequences: A110206 A110207 A110208 * A110210 A110211 A110212


KEYWORD

easy,nonn


AUTHOR

Jonathan Vos Post, Sep 06 2005


STATUS

approved



