|
| |
|
|
A094663
|
|
Prime numerators of the sums of the ratios of consecutive primes.
|
|
0
| | |
|
|
|
OFFSET
| 2,1
|
|
|
COMMENTS
| Sum of reciprocals = 0.5577902661277818841795751911..
|
|
|
FORMULA
| If a(n) = Sum(prime(k)/prime(k+1), k=1..n)) is prime.
|
|
|
EXAMPLE
| 2/3 + 3/5 +5/7 + 7/11 = 3023/1155. 3023 is prime, the third entry in the sequence.
|
|
|
MATHEMATICA
| Select[Numerator/@Accumulate[First[#]/Last[#]&/@ Partition[Prime[ Range[50]], 2, 1]], PrimeQ] (* From Harvey P. Dale, Apr 23 2011 *)
|
|
|
PROG
| (PARI) consecpr2(n) = { s=0; y=0; forprime(x=2, n, y+=x/nextprime(x+1); z=numerator(y); s+=1./z; if(isprime(z), print1(z", ")) ); print(); print(s) }
|
|
|
CROSSREFS
| Sequence in context: A013107 A172028 A024229 * A091688 A073444 A082259
Adjacent sequences: A094660 A094661 A094662 * A094664 A094665 A094666
|
|
|
KEYWORD
| frac,nonn
|
|
|
AUTHOR
| Cino Hilliard (hillcino368(AT)gmail.com), Jun 06 2004
|
|
|
EXTENSIONS
| The next term is too large to include.
|
| |
|
|
