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A097501
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p^q + q^p for consecutive pairs of twin primes p and q.
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0
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368, 94932, 36314872537968, 244552822542936127033092, 2177185942561672462146321298650240665136431700, 2246585380039521951243337580678537047744572047581514711375688196554564
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,1
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COMMENTS
| 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)?
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EXAMPLE
| Consider the second twin prime pair (5,7). 5^7 + 7^5 = 94932, the 2-nd entry.
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MATHEMATICA
| lst={}; Do[p=Prime[n]; If[PrimeQ[q=p+2], a=(p^q+q^p); AppendTo[lst, a]], {n, 2*4!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Aug 16 2009]
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PROG
| (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", ")))
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CROSSREFS
| Cf. A051442.
Sequence in context: A142579 A098823 A173055 * A062041 A205730 A183351
Adjacent sequences: A097498 A097499 A097500 * A097502 A097503 A097504
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KEYWORD
| nonn
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AUTHOR
| Cino Hilliard (hillcino368(AT)gmail.com), Aug 25 2004
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