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 A320335 Numerators of the fractions a(0)/(a(1) - a(0)), a(1)/(a(2) - a(1)), a(2)/(a(3) - a(2)), ... such that the sum Sum_{n>=1} a(n-1)/(a(n) - a(n-1)) has the concatenation of these numerators, starting from a(1), as decimal part. Case a(0) = 1, a(1) = 4. 11
 1, 4, 41, 89814, 98285430640360, 22352043009017562549812304739324022523 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS It appears that fractions of this kind with a(0)=1 exist only for a(1) equal to 4 (this sequence) and 13 (A320336). Next term has 98 digits. - Giovanni Resta, Oct 11 2018 LINKS Table of n, a(n) for n=0..5. EXAMPLE 1/(4-1) = 0.3333... At the beginning instead of 4 we have 3 as first decimal digit. Adding the second term this is fixed. 1/(4-1) + 4/(41 - 4) = 0.441441... 1/(4-1) + 4/(41 - 4) + 41/(89814 - 41) = 0.44189814891 ... The sum is 0.4 41 89814 98285430640360 ... MAPLE P:=proc(q, h) local a, b, d, t, x, n; x:=1; a:=1/(h-1); b:=ilog10(h-1)+1; d:=h; print(d); t:=h; for n from h+1 to q do if trunc(evalf(a+t/(n-t), 100)*10^(b+ilog10(n)+1))=d*10^(ilog10(n)+1)+n then b:=b+ilog10(n)+1; d:=d*10^(ilog10(n)+1)+n; a:=a+t/(n-t); t:=n; x:=n+1; print(n); fi; od; end: P(10^10, 4); CROSSREFS Cf. A302932, A302933, A303388, A304285, A304286, A304287, A304288, A304289, A305661, A305662, A305663, A305664, A305665, A305666, A320306, A320307, A320308, A320309, A320336. Sequence in context: A333731 A326899 A022500 * A076652 A078288 A349455 Adjacent sequences: A320332 A320333 A320334 * A320336 A320337 A320338 KEYWORD nonn,base AUTHOR Paolo P. Lava, Oct 11 2018 EXTENSIONS a(4)-a(5) from Giovanni Resta, Oct 11 2018 STATUS approved

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Last modified May 19 12:15 EDT 2024. Contains 372692 sequences. (Running on oeis4.)