A072580 -id:A072580 - cp's OEIS frontend

A072577 Numbers k such that k and the k-th prime have the same number of 0's in their binary representation.

5, 6, 20, 22, 24, 28, 31, 32, 34, 37, 41, 42, 49, 50, 67, 68, 81, 82, 84, 88, 89, 93, 94, 138, 139, 140, 141, 142, 143, 147, 151, 157, 165, 192, 194, 198, 200, 202, 206, 207, 232, 236, 241, 262, 265, 270, 271, 284, 285, 295, 301, 328, 329, 332, 333, 337

Offset: 1

Reinhard Zumkeller, Jun 23 2002

			In binary representation 20 and A000040(20) = 71 have three 0's: 13 = '10100' and 71 = '1000111', therefore 20 is a term.

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

Cf. A023416, A035103, A049084, A071600, A072578, A072579, A072580.

q[k_] := DigitCount[k, 2, 0] == DigitCount[Prime[k], 2, 0]; Select[Range[350], q] (* Amiram Eldar, Jul 28 2025 *)

A023416(a(n)) = A023416(A072580(n)) = A035103(n).

a(n) = A049084(A072580(n)).

A072581 a(n) = A000040(A072578(n)).

Original entry on oeis.org

19, 53, 139, 193, 311, 313, 409, 577, 641, 719, 787, 809, 1033, 1061, 1097, 1171, 1193, 1289, 1627, 1637, 1657, 1669, 1693, 1699, 1747, 1811, 1877, 1889, 2083, 2089, 2153, 2161, 2179, 2203, 2213, 2273, 2311, 2659, 2689, 2753, 3169, 3677, 3727, 3733

Offset: 1

Reinhard Zumkeller, Jun 23 2002

			In binary representation 80 = '1010000' has five 0's and A000040(80) = 409 = '110011001' has five 1's: therefore 409 is a term.

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

Cf. A000040, A000120, A014499, A023416, A072439, A072578, A072580, A072582, A072584.

With[{m = 600}, Select[Transpose[{Range[m], Prime[Range[m]]}], DigitCount[First[#], 2, 0] == DigitCount[Last[#], 2, 1] &]][[;; , 2]] (* Amiram Eldar, Jul 28 2025 *)

A000120(a(n)) = A023416(A072578(n)) = A014499(n).

A072582 a(n) = A000040(A072579(n)).

Original entry on oeis.org

2, 17, 41, 101, 157, 179, 181, 197, 227, 229, 271, 277, 293, 347, 349, 373, 397, 401, 449, 563, 571, 587, 601, 619, 647, 661, 757, 797, 811, 821, 829, 853, 929, 947, 953, 971, 977, 997, 1039, 1103, 1129, 1213, 1231, 1237, 1303, 1307, 1409, 1433, 1459

Offset: 1

Reinhard Zumkeller, Jun 23 2002

			In binary representation 70 = '1000110' has three 1's and A000040(70) = 349 = '101011101' has three 1's: therefore 349 is a term.

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

Cf. A000040, A000120, A023416, A035103, A072439, A072579, A072580, A072581, A072584.

With[{m = 300}, Select[Transpose[{Range[m], Prime[Range[m]]}], DigitCount[First[#], 2, 1] == DigitCount[Last[#], 2, 0] &]][[;; , 2]] (* Amiram Eldar, Jul 28 2025 *)

A023416(a(n)) = A000120(A072579(n)) = A035103(n).

A072584 a(n) = A000040(A072583(n)).

Original entry on oeis.org

3, 7, 23, 29, 31, 37, 43, 47, 59, 61, 103, 109, 137, 149, 151, 163, 167, 173, 191, 199, 223, 233, 239, 241, 251, 257, 263, 307, 317, 359, 367, 379, 383, 431, 439, 443, 463, 467, 479, 499, 503, 509, 541, 557, 569, 599, 607, 613, 617, 631, 643, 653, 659, 673

Offset: 1

Reinhard Zumkeller, Jun 23 2002

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

Cf. A000040, A072439, A072580, A072581, A072582, A072583.

With[{m = 120}, Select[Transpose[{Range[m], Prime[Range[m]]}], Intersection @@ DigitCount[#, 2] == {} &]][[;; , 2]] (* Amiram Eldar, Jul 28 2025 *)

cp's OEIS Frontend

A072577 Numbers k such that k and the k-th prime have the same number of 0's in their binary representation.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

Formula

A072581 a(n) = A000040(A072578(n)).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

Formula

A072582 a(n) = A000040(A072579(n)).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

Formula

A072584 a(n) = A000040(A072583(n)).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica