A308633 Continued fraction for the decimal expansion of the concatenation of the terms of A051699 (distance from n to closest prime).

0, 4, 1, 3, 5, 9, 1, 2, 2, 4, 7, 1, 246, 1, 2, 2, 1, 116363868, 3, 1, 1, 1, 3, 4, 282, 1, 1, 1, 2, 1, 8, 2, 1, 1, 1, 1, 7, 10, 7, 1, 2, 1, 6, 2, 1, 2, 7, 2, 11, 1, 3, 1, 4, 1, 4, 1, 3, 5, 9, 1, 1, 1, 3, 3, 1, 3, 2, 1, 5, 3, 3, 1, 32, 1, 1, 15, 3, 1, 1, 11, 9, 1

Offset: 0

Author

Paolo P. Lava, Jun 17 2019

Keywords

• base
• cofr
• nonn
• easy

Comments

Continued fraction for .2100101012101012101012101232101012321... (see A051699).

Very high value for a(17) = 116363868. This should imply that using the first 16 terms we have a good rational approximation of this decimal expansion: 131256182/624999375 is ok up to the 25th decimal digit.

Crossrefs

Cf. A030168, A051699.

Programs

Maple

Digits:=200: with(numtheory): P:=proc(q) local a,b,n; a:=21;
for n from 2 to q do if isprime(n) then a:=10*a; else
b:=min(nextprime(n)-n,n-prevprime(n)); a:=a*10^length(b)+b; fi; od;
op(convert(evalf(a/10^length(a)),confrac,100)); end: P(200);