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

Author

Paolo P. Lava, May 25 2015

Keywords

• nonn
• cons

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,...].

Examples

			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...
		

Crossrefs

Cf. A045926, A194181, A194182.

Programs

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);