A072583 Numbers k with the property that there is no match when comparing the numbers of 0's and 1's in the binary representations of k and the k-th prime.

2, 4, 9, 10, 11, 12, 14, 15, 17, 18, 27, 29, 33, 35, 36, 38, 39, 40, 43, 46, 48, 51, 52, 53, 54, 55, 56, 63, 66, 72, 73, 75, 76, 83, 85, 86, 90, 91, 92, 95, 96, 97, 100, 102, 104, 109, 111, 112, 113, 115, 117, 119, 120, 122, 123, 124, 126, 127, 129, 130, 131, 132, 133

Offset: 1

Author

Reinhard Zumkeller, Jun 23 2002

Keywords

• nonn
• base
• easy

Comments

In other words, A000120(k) <> A000120(A000040(k)) and A000120(k) <> A023416(A000040(k)) and A023416(k) <> A000120(A000040(k)) and A023416(k) <> A023416(A000040(k)).

A000120(k) <> A014499(k) and A000120(k) <> A035103(k) and A023416(k) <> A014499(k) and A023416(k) <> A035103(k).

Examples

			k = 40 = '101000', A000040(40) = 173 = '10101101'.
		

Links

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

Crossrefs

Cf. A000040, A000120, A014499, A023416, A035103, A049084, A071600, A072577, A072578, A072579, A072584.

Programs

Mathematica

With[{m = 150}, Select[Transpose[{Range[m], Prime[Range[m]]}], Intersection @@ DigitCount[#, 2] == {} &]][[;; , 1]] (* Amiram Eldar, Jul 28 2025 *)

Formula

a(n) = A049084(A072584(n)).