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A134125 Integral quotients of prime partial sums divided by the running count of summations. +0
6
5, 5, 7, 11, 16, 107, 338, 1011, 2249, 22582, 35989, 39167, 61019, 186504, 248776, 367842, 977511, 1790714, 7104697, 15450640, 42428590 (list; graph; listen)
OFFSET

1,1

COMMENT

With 1 summation, the partial sum is 2+3=5 and 5/1=5 is integer, added to sequence. With 2 summations, the partial sum is 2+3+5=10 and 10/2=5 is integer, added to the sequence. After 3 summations, 2+3+5+7=17 and 17/3=5.6.. is not integer, no contribution to the sequence.

These are all integers of the form a(n)=A007504(k+1)/k, occurring at k=A134126(n). Similar to A050248, which looks at A007504(k)/k. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 23 2007

EXAMPLE

a(1)=5 because 2+3=5 and 5/1=5, an integral quotient. a(3)= A007504(5)/4 = 28/4 =7. a(4)=A007504(8)/7 = 77/7 =11.

PROGRAM

UBASIC: 10 'primes using counters 20 N=3:C=1:R=5:print 2; 3, 5 30 A=3:S=sqrt(N) 40 B=N\A 50 if B*A=N then N=N+2:goto 30 60 A=A+2:O=A 70 if A<=sqrt(N) then 40 80 C=C+1 90 R=R+N:T=R/C:U=R-N 100 if T=int(T) then print C; U; N; R; T:stop 110 N=N+2:goto 30

CROSSREFS

Cf. A134126, A134127, A134128, A134129.

Sequence in context: A120220 A153105 A154583 this_sequence A097996 A033300 A134130

Adjacent sequences: A134122 A134123 A134124 this_sequence A134126 A134127 A134128

KEYWORD

more,nonn

AUTHOR

Enoch Haga (Enokh(AT)comcast.net), Oct 09 2007

EXTENSIONS

a(21) from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 23 2007

Edited by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 17 2009

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Last modified December 20 00:58 EST 2009. Contains 171054 sequences.


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