1,1

Short table: Count of 1: 2+3=5, and 5/1=5 add to sequence Count of 2: 5+5=10, and 10/2=5, add to sequence Count of 3: 10+7=17, and 17/3=5.6+ not integral, don't add Count of 4: 17+11=28, and 28/4=7, add to sequence Etc.

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

Begin at the count of 1 with 2, add 3, sum to 5; then add next prime 5 to obtain 10, add the next prime 7 to obtain 17, and continue. At the count of 4 the cumulative sum is 17 to which 11, the next prime is added, summing to 28. After each count divide by the index of the count, e.g., 28/4=7. If the quotient is integral add to the sequence (at the count of 3 the quotient is not integral so is not a member of the sequence).

a(1)=5 because 2+3=5, and 5/1=5, an integral quotient. a(3)=10+7=17, and 17/3 = 5.6+ so is not integral and is not added to the sequence.

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

Cf. A134126 A134127 A134128 A134129.

Sequence in context: A028278 A095943 A120220 this_sequence A097996 A033300 A134130

Adjacent sequences: A134122 A134123 A134124 this_sequence A134126 A134127 A134128

easy,more,nonn,uned

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

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