A054901 Numbers of the form 2^i*5^j where i+j is even.

1, 4, 10, 16, 25, 40, 64, 100, 160, 250, 256, 400, 625, 640, 1000, 1024, 1600, 2500, 2560, 4000, 4096, 6250, 6400, 10000, 10240, 15625, 16000, 16384, 25000, 25600, 40000, 40960, 62500, 64000, 65536, 100000, 102400, 156250, 160000, 163840

Offset: 1

Author

Henry Bottomley, May 23 2000

Keywords

• easy
• nonn

Comments

m is in the sequence iff m/10 is already in the sequence or m is a power of 4 or 25.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A028260 and A003592.

Cf. A000302, A009969, A054774.

Programs

Mathematica

max = 200000; Reap[Do[k = 2^i*5^j; If[k <= max && EvenQ[i + j], Sow[k]], {i, 0, Log[2, max] // Ceiling}, {j, 0, Log[5, max] // Ceiling}]][[2, 1]] // Union (* Amiram Eldar, Feb 18 2021 after Jean-François Alcover at A036667 *)

Formula

Sum_{n>=1} 1/a(n) = 55/36. - Amiram Eldar, Feb 18 2021