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 A339499 Decimal expansion of the generating constant for the composite numbers. 0
 4, 5, 8, 9, 2, 4, 6, 1, 2, 6, 6, 3, 7, 9, 8, 6, 1, 7, 1, 3, 5, 8, 1, 0, 2, 4, 2, 0, 7, 3, 5, 0, 7, 0, 7, 3, 6, 9, 2, 7, 4, 1, 4, 8, 3, 3, 8, 6, 1, 6, 7, 4, 8, 3, 0, 6, 5, 0, 1, 9, 9, 9, 5, 7, 4, 4, 4, 9, 7, 6, 6, 4, 4, 8, 6, 2, 2, 8, 2, 4, 0, 9, 9, 8, 0, 6, 1, 3, 1, 6, 1, 4, 4, 9, 5, 3, 5, 6, 0, 8 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The integer parts of the sequence having this constant as starting value and thereafter a(n+1) = (frac(a(n))+1) * floor(a(n)), where floor and frac are integer and fractional part, are exactly the sequence of the composite numbers: see the Grime-Haran Numberphile video for details. LINKS James Grime and Brady Haran, 2.920050977316, Numberphile video, Nov 26 2020. FORMULA Sum_{k >= 1} (c(k) - 1)/(c(1) * c(2) * ... * c(k-1)), where c(k) is the k-th composite number. EXAMPLE 4.5892461266379861713581024207350707369274148338616748... PROG (Python) from mpmath import * #high precision computations                      #nsum function from sympy import * # to generate prime numbers mp.dps = 10000 #function that generates constant that encodes all composite numbers #cnt - number of prime numbers def composconst(cnt):     if cnt==1:         return 4-1     primlist=list()     i=0     while (i

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Last modified May 7 10:17 EDT 2021. Contains 343649 sequences. (Running on oeis4.)