The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A051838 Numbers k such that sum of first k primes divides product of first k primes. 19
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; text; internal format)
OFFSET
1,2
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)
FORMULA
From Reinhard Zumkeller, Oct 03 2011: (Start)
A002110(a(n)) mod A007504(a(n)) = 0.
A116536(n) = A002110(a(n)) / A007504(a(n)). (End)
EXAMPLE
Sum of first 8 primes is 77 and product of first 8 primes is 9699690. 77 divides 9699690 therefore a(3)=8.
MATHEMATICA
p = Prime@ Range@ 250; Flatten@ Position[ Mod[ First@#, Last@#] & /@ Partition[ Riffle[ Rest[ FoldList[ Times, 1, p]], Accumulate@ p], 2], 0] (* Harvey P. Dale, Dec 19 2010 *)
PROG
(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
(PARI) for(n=1, 100, P=prod(i=1, n, prime(i)); S=sum(i=1, n, prime(i)); if(!(P%S), print1(n, ", "))) \\ Derek Orr, Jul 19 2015
(PARI) isok(n) = my(p = primes(n)); (vecprod(p) % vecsum(p)) == 0; \\ Michel Marcus, Dec 20 2018
(GAP) P:=Filtered([1..2000], IsPrime);;
Filtered([1..Length(P)], n->Product([1..n], i->P[i]) mod Sum([1..n], i->P[i])=0); # Muniru A Asiru, Dec 20 2018
CROSSREFS
A116536 gives the quotients, A140763 the divisors and A159578 the dividends.
Sequence in context: A194427 A335048 A185954 * A076792 A146939 A181540
KEYWORD
nonn
AUTHOR
G. L. Honaker, Jr., Dec 12 1999
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 27 00:30 EDT 2024. Contains 372847 sequences. (Running on oeis4.)