The OEIS is supported by the many generous donors to the OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A339061 Least integer j such that H(k+j)>=n+1, where k is the least integer to satisfy H(k)>=n, and H(k) is the sum of the first k terms of the harmonic series. 0
 1, 3, 7, 20, 52, 144, 389, 1058, 2876, 7817, 21250, 57763, 157017, 426817, 1160207, 3153770, 8572836, 23303385, 63345169, 172190019, 468061001, 1272321714, 3458528995, 9401256521, 25555264765, 69466411833, 188829284972, 513291214021 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS FORMULA a(n) ~ (e-1)*e^(n-gamma), where e is Euler's number and gamma is the Euler-Mascheroni constant. Conjecture: a(n) = floor(1/2 + e^(n-gamma+1)) - floor(1/2 + e^(n-gamma)) for n > 1 where e is Euler's number and gamma is the Euler-Mascheroni constant. - Adam Hugill, Nov 06 2022 EXAMPLE Define H(0)=0, H(k) = Sum_{i=1..k} 1/i for k=1,2,3,... a(0)=1: To reach n+1 from n=0 requires 1 additional term of the harmonic partial sum: H(0+1) = H(0) + 1/1 = H(1) = 1. a(1)=3: To reach n+1 from n=1 requires 3 additional terms of the harmonic partial sum: H(1+3) = H(1) + 1/(1+1) + 1/(1+2) + 1/(1+3) = H(4) = 2.08333.... a(2)=7: To reach n+1 from n=2 requires 7 additional terms of the harmonic partial sum: H(4+7) = H(4) + 1/(4+1) + 1/(4+2) + ... + 1/(4+6) + 1/(4+7) = H(11) = 3.01987.... a(3)=20: To reach n+1 from n=3 requires 20 additional terms of the harmonic partial sum: H(11+20) = H(11) + 1/(11+1) + 1/(11+2) + ... + 1/(11+19) + 1/(11+20) = H(31) = 4.02724.... PROG (R) #set size of search space Max=10000000 #initialize sequence to empty seq=vector(length=0) #initialize partial sum to 0 partialsum=0 k=1 n=1 for(i in 1:Max){ partialsum=partialsum+1/i if(partialsum>=n){ seq=c(seq, k) k=0 n=n+1 } k=k+1 } #print sequence numbers below Max seq CROSSREFS First differences of A004080. Cf. A001113 (e), A001620 (gamma). Cf. A001008/A002805 (harmonic numbers). Some sequences in the same spirit as this: A331028, A002387, A004080. Sequence in context: A230352 A271894 A066315 * A058499 A003097 A109220 Adjacent sequences: A339058 A339059 A339060 * A339062 A339063 A339064 KEYWORD nonn AUTHOR Matthew J. Bloomfield, Dec 21 2020 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.

Last modified March 24 09:16 EDT 2023. Contains 361470 sequences. (Running on oeis4.)