A258271 Decimal expansion of the sum of the reciprocal of the squares of the numbers whose digits are all even.

0, 3, 6, 6, 3, 6, 0, 0, 3, 9, 7, 1, 9, 5, 2, 3, 2, 9, 5, 1, 7, 1, 8, 8, 2, 5, 0, 8, 9, 6, 7, 4, 1, 2, 4, 2, 6, 6, 2, 5, 1, 7, 3, 9, 5, 0, 3, 4, 2, 1, 1, 8, 7, 6, 0, 0, 2, 0, 0, 7, 1, 1, 3, 5, 0, 8, 5, 2, 8, 3, 3, 3, 2, 9, 3, 4, 9, 5, 1, 5, 7, 5, 8, 4, 4, 6, 5

Offset

1,2

Comments

A rational approximation (correct up to the 9th decimal digit) is 22781/62182.

Continued fraction: [0, 2, 1, 2, 1, 2, 3, 3, 1, 8, 5, 2, 1, 14,...].

Links

Table of n, a(n) for n=1..87.

Example

Decimal expansion of Sum_{k=1..oo}{1/A045926(k)^2} = 1/2^2 + 1/4^2 + 1/6^2 + 1/8^2 + 1/22^2 + 1/24^2 + 1/26^2 + ... = 0.3663600397195232951718825089674124266251739503421187600...

Maple

P:=proc(q) local a, b, k, ok, n; a:=0; for n from 2 by 2 to q do ok:=1; b:=n;
for k from 1 to ilog10(n)+1 do if (b mod 10)=0 or ((b mod 10) mod 2)=1 then ok:=0;
break; else b:=trunc(b/10); fi; od; if ok=1 then a:=a+(1/n)^2; fi; od;
print(evalf(a, 200)); end: P(10^9);

Crossrefs

Cf. A045926, A194181, A194182.

Sequence in context: A309448 A354952 A016662 * A105396 A247685 A372367

Adjacent sequences: A258268 A258269 A258270 * A258272 A258273 A258274

Keyword

nonn,cons

Author

Paolo P. Lava, May 25 2015

Status

approved