A110208 1 + sum of first n semiprimes.

1, 5, 11, 20, 30, 44, 59, 80, 102, 127, 153, 186, 220, 255, 293, 332, 378, 427, 478, 533, 590, 648, 710, 775, 844, 918, 995, 1077, 1162, 1248, 1335, 1426, 1519, 1613, 1708, 1814, 1925, 2040, 2158, 2277, 2398, 2520, 2643, 2772, 2905, 3039, 3180, 3322, 3465

Offset

0,2

Comments

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.

Links

Table of n, a(n) for n=0..48.

Formula

a(0) = 1; for n>0, a(n) = 1 + A062198(n).

Mathematica

Accumulate[Join[{1}, Select[Range[200], PrimeOmega[#]==2&]]] (* Harvey P. Dale, Apr 29 2018 *)

Crossrefs

Cf. A001358, A062198, A110209, A110226.

Sequence in context: A304502 A190743 A331133 * A034308 A032527 A212978

Adjacent sequences: A110205 A110206 A110207 * A110209 A110210 A110211

Keyword

easy,nonn

Author

Jonathan Vos Post, Sep 06 2005

Status

approved