|
Search: id:A097501
|
|
|
| A097501 |
|
p^q + q^p for consecutive pairs of twin primes p and q. |
|
+0
1
|
|
| 368, 94932, 36314872537968, 244552822542936127033092, 2177185942561672462146321298650240665136431700, 2246585380039521951243337580678537047744572047581514711375688196554564
(list; graph; listen)
|
|
|
OFFSET
|
2,1
|
|
|
COMMENT
|
Except for the first term, 6 divides seq(n). Let p = 3k+2 for odd k since k even implies p even, a contradiction. Then p = 6m + 5 and q = 6m+7 = 6m1 + 1. So p^q+q^p = (6m+5)^(6m1+1) + (6m1+1)^(6m+5) = 6H + 5^odd + 1^odd. Now 5 = (6-1) and (6-1)^odd + 1 = 6G -1 + 1 = 6G as stated. Are 3 and 17 the only primes in A051442(n)?
|
|
EXAMPLE
|
Consider the second twin prime pair (5,7). 5^7 + 7^5 = 94932, the 2-nd entry.
|
|
PROGRAM
|
(PARI) f(n) = for(x=1, n, p=prime(x); q=prime(x+1); if(q-p==2, v=p^q+q^p; print1(v", ")))
|
|
CROSSREFS
|
Cf. A051442.
Sequence in context: A067891 A142579 A098823 this_sequence A062041 A108772 A102618
Adjacent sequences: A097498 A097499 A097500 this_sequence A097502 A097503 A097504
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Cino Hilliard (hillcino368(AT)gmail.com), Aug 25 2004
|
|
|
Search completed in 0.002 seconds
|
