cp's OEIS Frontend

First differences are the sequence of semiprimes (A001358). Hence a(n) is the least positive sequence whose first differences are the sequence of semiprimes. Primes in this sequence include: a(1) = 5, a(2) = 11, a(6) = 59, a(9) = 127, a(14) = 293, a(33) = 1613. Semiprimes in this sequence include: a(17) = 427 = 7 * 61, a(18) = 478 = 2 * 239, a(19) = 533 = 13 * 41, a(26) = 995 = 5 * 199, a(27) = 1077 = 3 * 359, a(35) = 1814 = 2 * 907, a(42) = 2643 = 3 * 881, a(45) = 3039 = 3 * 1013.

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.