Revision History for A123129
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing all changes.
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#7 by Alois P. Heinz at Wed Aug 04 18:15:58 EDT 2021
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#6 by Alois P. Heinz at Wed Aug 04 18:15:55 EDT 2021
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#5 by Alois P. Heinz at Wed Aug 04 18:15:37 EDT 2021
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#4 by G. C. Greubel at Wed Aug 04 18:09:03 EDT 2021
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#3 by G. C. Greubel at Wed Aug 04 18:08:53 EDT 2021
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| NAME
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(n + n-th difference between consecutive primes) raised to power n-1.
a(n) = ( n + prime(n+1) - prime(n) )^(n-1).
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| LINKS
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G. C. Greubel, <a href="/A123129/b123129.txt">Table of n, a(n) for n = 1..350</a>
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| FORMULA
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a(n) = ( n + prime(n+1) - prime(n) )^(n-1) = ( n + A001223(n) )^(n-1)).
From G. C. Greubel, Aug 04 2021: (Start)
a(n) = (A014690(n) - prime(n))^(n-1) = (A095116(n+1) - prime(n))^(n-1).
a(n) = (prime(n+1) - A014689(n))^(n-1). (End)
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| MATHEMATICA
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Table[(n +Prime[n+1] -Prime[n])^(n-1), {n, 1, 30}] (* G. C. Greubel, Aug 04 2021 *)
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| PROG
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(PARI) for(n=1, , 25, , print1((( (prime(n+1)-) -prime(n)+) +n)^(n-1), ", "))), ", "))
(Sage) [(n + nth_prime(n+1) - nth_prime(n))^(n-1) for n in (1..30)] # G. C. Greubel, Aug 04 2021
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| CROSSREFS
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Cf. A001223, A014690, A095116.
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| STATUS
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approved
editing
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#2 by N. J. A. Sloane at Fri May 11 03:00:00 EDT 2007
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| NAME
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(n + nthn-th difference between consecutive primes) raised to power n-1.
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| KEYWORD
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nonn,new
nonn
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#1 by N. J. A. Sloane at Mon Oct 09 03:00:00 EDT 2006
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| NAME
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(n + nth difference between consecutive primes) raised to power n-1.
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| DATA
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1, 4, 25, 512, 2401, 100000, 531441, 35831808, 2562890625, 5159780352, 2015993900449, 17592186044416, 129746337890625, 20822964865671168, 3243919932521508681, 136880068015412051968, 288441413567621167681
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| OFFSET
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1,2
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| LINKS
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Sergio Silva, <a href="http://ginasiomental.no.sapo.pt/materialc/mteste/teste.htm">Teste Numerico</a>.
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| FORMULA
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a(n) = ( n + prime(n+1) - prime(n) )^(n-1) = ( n + A001223(n) )^(n-1)
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| PROG
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(PARI) for(n=1, 25, print1((prime(n+1)-prime(n)+n)^(n-1), ", "))
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| KEYWORD
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nonn,new
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| AUTHOR
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Herman Jamke (hermanjamke(AT)fastmail.fm), Sep 30 2006
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| STATUS
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approved
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