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 A338699 Sequence A is the primes.  Sequence B is the "smallest" sequence of nondecreasing powers of two whose sum over the first N terms is at least equal to the sum over the first N terms of Sequence A.  a(n) is the amount by which the sum of the first n terms of Sequence B exceeds the sum of the first n terms of Sequence A. 2
 0, 1, 0, 1, 6, 9, 8, 5, 14, 17, 18, 13, 4, 25, 42, 53, 58, 61, 58, 51, 42, 27, 8, 47, 78, 105, 130, 151, 170, 185, 186, 183, 174, 163, 142, 119, 90, 55, 16, 99, 176, 251, 316, 379, 438, 495, 540, 573, 602, 629, 652, 669, 684, 689, 688, 681, 668, 653, 632, 607, 580 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS The definition is due to Jack Brennen. LINKS Rémy Sigrist, Table of n, a(n) for n = 1..10000 Kevin Ryde, Piecewise-Linear Above Cumulative Primes (and LaTeX+PGF source) EXAMPLE We want to produce prime numbers out of nondecreasing "blocks" of powers of 2. Each time we use one block in addition to the remains of the previous block. To get 2, we need a block of 2. So a(1) = 2-2 = 0. To get 3, we need a block of 4. So a(2) = 4-3 = 1. To get 5, we need a block of 4 in addition to the remains of the previous block. So a(3) = 4+1-5 = 0. PROG (PARI) accum=0; inc=2; forprime(p=2, 99, while(accum+inc

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Last modified January 21 22:08 EST 2022. Contains 350480 sequences. (Running on oeis4.)