|
| |
|
|
A097589
|
|
a(n)=sum from i=1 to n of the Fortunate numbers (A005235).
|
|
0
| |
|
|
3, 8, 15, 28, 51, 68, 87, 110, 147, 208, 275, 336, 407, 454, 561, 620, 681, 790, 879, 982, 1061, 1212, 1409, 1510, 1613, 1846, 2069, 2196, 2419, 2610, 2773, 3002, 3645, 3884, 4041, 4208, 4647, 4886, 5085, 5276, 5475, 5858, 6091, 6842, 7155, 7928, 8535, 8848
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
COMMENTS
| The primes and fortunate numbers in the partial sum of the fortunate numbers (A005235): primes begin: 3, 1061, 1409, 1613, 2069, 6091; fortunate numbers in partial sum begin: 3, 1061, 1409, 1613, 6091, and these subsequences are not disjoint. [From Jonathan Vos Post (jvospost3(AT)gmail.com), Jan 27 2010]
|
|
|
FORMULA
| Let F(n) := a(n)/A007504(n). Conjecture: as n tends to infinity F(n) tends to pi/2 with pi=3.14159......
|
|
|
MATHEMATICA
| NextPrime[ n_Integer] := Block[{k}, k = n + 1; While[ !PrimeQ[ k ], k++ ]; k ]; Fortunate[ n_Integer] := Block[{p = Product[ Prime[i], {i, 1, n} ] + 1, q}, q = NextPrime[p]; q - p + 1 ]; t = Table[ Fortunate[ n ], {n, 1, 48}]; Table[Plus @@ Take[t, n], {n, 48}] (from Robert G. Wilson v Sep 04 2004)
|
|
|
CROSSREFS
| Cf. A005235 A007504.
Sequence in context: A047873 A036419 A054107 * A015631 A116686 A135350
Adjacent sequences: A097586 A097587 A097588 * A097590 A097591 A097592
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Pierre CAMI (pierre-cami(AT)bbox.fr), Aug 29 2004
|
|
|
EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 04 2004
|
| |
|
|
