A185066 Bershadskii's ln-sequence.

7, 14, 28, 35, 49, 55, 69, 87, 94, 112, 126, 133, 147, 165, 183, 190, 207, 221, 228, 246, 260, 278, 299, 313, 320, 333, 340, 354, 381, 394, 412, 419, 442, 449, 467, 485, 499, 517, 535, 542, 565, 572, 586, 592, 617, 642, 656, 663

Offset

1,1

Comments

Bershadskii: Let us take, as a first step, logarithms of the gaps for the sequence of prime numbers.... Then, let us compute cumulative sum of these logarithms as a second step. Then, we will multiply each value in the cumulative sum by 10 and will replace each of the obtained values by a natural number which is nearest to it.

Links

G. C. Greubel, Table of n, a(n) for n = 1..5000

A. Bershadskii, Hidden periodicity in the sequence of prime numbers, arXiv:1102.3648 [math.NT], 2011.

Maple

Digits := 20 ; A185066 := proc(n) x := 0 ; for i from 1 to n+1 do x := x+log(ithprime(i+1)-ithprime(i)) ; end do; round(10*x) ; end proc: # R. J. Mathar, Mar 16 2011

Mathematica

Rest[Floor[#+1/2]&/@(10#&/@Accumulate[Log[Differences[Prime[Range[ 100]]]]])] (* Harvey P. Dale, Aug 18 2011 *)

Crossrefs

Sequence in context: A104599 A115874 A083495 * A089644 A178335 A158204

Adjacent sequences: A185063 A185064 A185065 * A185067 A185068 A185069

Keyword

nonn,easy

Author

Jonathan Vos Post, Feb 18 2011

Status

approved