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A051838
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Numbers n such that sum of first n primes divides product of first n primes.
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13
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1, 3, 8, 13, 23, 38, 39, 41, 43, 48, 50, 53, 56, 57, 58, 66, 68, 70, 73, 77, 84, 90, 94, 98, 126, 128, 134, 140, 143, 145, 149, 151, 153, 157, 160, 164, 167, 168, 172, 174, 176, 182, 191, 194, 196, 200, 210, 212, 215, 217, 218, 219, 222, 225, 228, 229
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| A002110(a(n)) mod A007504(a(n)) = 0, A116536(n) = A002110(a(n)) / A007504(a(n)). [Reinhard Zumkeller, Oct 03 2011]
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LINKS
| T. D. Noe, Table of n, a(n) for n = 1..1000
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EXAMPLE
| Sum of first 8 primes is 77 and product of first 8 primes is 9699690. 77 divides 9699690 therefore a(3)=8.
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MATHEMATICA
| p = Prime@ Range@ 250; Flatten@ Position[ Mod[ First@#, Last@#] & /@ Partition[ Riffle[ Rest[ FoldList[ Times, 1, p]], Accumulate@ p], 2], 0]
[From Harvey P. Dale, Dec. 19, 2010]
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PROG
| via Wolfram Alpha, input: (prod(prime(n), n=1..229)) mod (sum(prime(n), n=1..229)) for example [from Bill McEachen, Feb 23 2011]
(Haskell)
import Data.List (elemIndices)
a051838 n = a051838_list !! (n-1)
a051838_list =
map (+ 1) $ elemIndices 0 $ zipWith mod a002110_list a007504_list
-- Reinhard Zumkeller, Oct 03 2011
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CROSSREFS
| Cf. A007504, A002110. A116536 gives the quotients, A140763 the divisors and A159578 the dividends. See also A159639.
Cf. A196415.
Sequence in context: A084535 A194427 A185954 * A076792 A146939 A181540
Adjacent sequences: A051835 A051836 A051837 * A051839 A051840 A051841
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KEYWORD
| nonn
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AUTHOR
| G. L. Honaker, Jr. (honak3r(AT)gmail.com), Dec 12 1999
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