A216442 Numbers of the form 2^i + 3^j + 5^k, where i, j, k >= 0.

3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 18, 20, 22, 24, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 38, 40, 42, 44, 46, 48, 50, 53, 54, 56, 58, 60, 64, 66, 68, 70, 72, 74, 78, 83, 84, 86, 87, 88, 90, 92, 94, 96, 98, 102, 107, 108, 110, 114, 116, 118, 122, 127

Offset: 1

Author

Robert G. Wilson v, Sep 20 2012

Keywords

• nonn

Comments

Conjecture: Unlike A004050, which has a limited set of integers expressible in more than one way, this set has no such limit.

Number of terms less than or equal to 10^k, k > 0: 8, 56, 238, 615, 1304, 2169, 3606, 5280, 7196, 10414, ....

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000
• Diego Marques and Alain Togbé, Fibonacci and Lucas numbers of the form 2^a + 3^b + 5^c, Proc. Japan Acad. Ser. A Math. Sci. 89(3): 47-50 (March 2013).

Crossrefs

Cf. A004050.

Programs

Mathematica

mx = 140; Union@ Flatten@ Table[2^i + 3^j + 5^k, {i, 0, Log[2, mx]}, {j, 0, Log[3, mx - 2^i]}, {k, 0, Log[5, mx - 2^i - 3^j]}]

Formula

There are O(log^3 x) terms of the sequence up to x. - Charles R Greathouse IV, Oct 28 2022