|
Search: id:A105554
|
|
|
| A105554 |
|
Primes whose indices are the sum of the first n+1 Fibonacci numbers. |
|
+0
1
|
|
| 2, 3, 7, 17, 37, 71, 137, 251, 457, 823, 1459, 2579, 4483, 7789, 13463, 23143, 39769, 67927, 115823, 196681, 333227, 563971, 951553, 1603471, 2696653, 4528921, 7594759, 12717701, 21275489, 35548187, 59328121, 98921047, 164781917
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
We avoid testing for existence in the script by beginning with x=1.
Sum[i=1 to n+1]F(i) = F(n+3) - 1. See equation (18) of the Weisstein reference. - Jonathan Vos Post (jvospost3(AT)gmail.com), May 05 2005
|
|
LINKS
|
Eric Weisstein's World of Mathematics, Fibonacci Number.
|
|
FORMULA
|
a(n) = prime(F(n+3) - 1) = A000040(A000045(n+3)-1). - Jonathan Vos Post (jvospost3(AT)gmail.com), May 05 2005
|
|
EXAMPLE
|
If n=0, Fibonacci(0)+Fibonacci(1)=1 and prime(1) = 2 the 0 + 1-th or 1-st entry.
if n=2, Fibonacci(0)+Fibonacci(1)+Fibonacci(2)+Fibonacci(3)=4 and prime(4)=7 the 2 + 1-th or third entry.
|
|
PROGRAM
|
(PARI) g(n) = s=0; for(x=1, n, s+=fibonacci(x); print1(prime(s)", "))
|
|
CROSSREFS
|
Sequence in context: A077007 A165804 A155548 this_sequence A145230 A135364 A051291
Adjacent sequences: A105551 A105552 A105553 this_sequence A105555 A105556 A105557
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Cino Hilliard (hillcino368(AT)gmail.com), May 03 2005
|
|
EXTENSIONS
|
Corrected by T. D. Noe (noe(AT)sspectra.com), Nov 15 2006
|
|
|
Search completed in 0.002 seconds
|
