cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

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

Views

Author

Reinhard Zumkeller, Jun 23 2002

Keywords

Examples

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

Links

Crossrefs

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

Programs

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

Formula

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

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

Original entry on oeis.org

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

Views

Author

Reinhard Zumkeller, Jun 23 2002

Keywords

Examples

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

Links

Crossrefs

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

Programs

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

Formula

A023416(a(n)) = A023416(A072580(n)) = A035103(n).
a(n) = A049084(A072580(n)).

A072578 In binary representation: k has the same number of 0's as the k-th prime has 1's.

Original entry on oeis.org

8, 16, 34, 44, 64, 65, 80, 106, 116, 128, 138, 140, 174, 178, 184, 193, 196, 209, 258, 259, 260, 263, 264, 266, 272, 280, 288, 290, 314, 316, 325, 326, 327, 328, 330, 338, 344, 385, 391, 402, 449, 514, 520, 521, 528, 544, 566, 570, 574, 578, 587, 590, 597
Offset: 1

Views

Author

Reinhard Zumkeller, Jun 23 2002

Keywords

Examples

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

Links

Crossrefs

Cf. A000120, A014499, A023416, A049084, A071600, A072577, A072579, A072581.

Programs

  • Mathematica
    Select[Range[600],DigitCount[#,2,0]==DigitCount[Prime[#],2,1]&] (* Harvey P. Dale, Jan 07 2014 *)

Formula

A000120(A072581(n)) = A023416(a(n)) = A014499(n).
a(n) = A049084(A072581(n)).

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.

Original entry on oeis.org

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

Views

Author

Reinhard Zumkeller, Jun 23 2002

Keywords

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

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)).
Showing 1-4 of 4 results.

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