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A070901
a(1)=1, a(n) is the smallest integer > a(n-1) such that the largest element in the simple continued fraction for S(n)=1/a(1)+1/a(2)+...+1/a(n) equals prime(n).
1
1, 3, 8, 85, 103, 349, 361, 429, 500, 505, 1832, 1895, 1996, 2195, 2202, 2290, 2531, 2575, 2688, 3040, 3189, 3280, 3792, 5103, 5151, 7712, 21398, 21914, 22472, 22603, 22814, 23184, 23375, 24368, 24370, 24545, 24812, 25015, 25262, 25613, 26171, 26680, 27376, 28761, 29355
OFFSET
1,2
LINKS
David A. Corneth, Table of n, a(n) for n = 1..1000 (first 157 terms from Robert Israel)
FORMULA
Sum_{k >= 1} 1/a(k) < 1.5.
EXAMPLE
The continued fraction for S(4)=1+1/3+1/8+1/85 is [1, 2, 7, 1, 6, 5, 1, 2] where the largest element is 7=prime(4).
MAPLE
S:= 1: R:= 1: j:= 1:
for n from 2 to 50 do
p:= ithprime(n);
for j from j+1 do
F:= NumberTheory:-ContinuedFraction(S+1/j);
if max(Term(F, all)) = p then break fi;
od;
R:= R, j; S:= S + 1/j;
od:
R; # Robert Israel, Jul 31 2026
PROG
(PARI) lista(n) = my(a=vector(n), s=1, t=1); a[1] = t; for(n=2, #a, my(m=prime(n)); s=s+1/t; t++; while(vecmax(contfrac(s+1/t))!=m, t++); a[n]=t); a
CROSSREFS
Sequence in context: A233175 A347920 A367273 * A079657 A136309 A266671
KEYWORD
nonn
AUTHOR
Benoit Cloitre, May 19 2002
EXTENSIONS
More terms from b-file made by Robert Israel. - David A. Corneth, Aug 01 2026
STATUS
approved