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.

Previous Showing 11-20 of 20 results.

A095280 Lower Wythoff primes, i.e., primes in A000201.

Original entry on oeis.org

3, 11, 17, 19, 29, 37, 43, 53, 59, 61, 67, 71, 79, 97, 101, 103, 113, 127, 131, 137, 139, 163, 173, 179, 181, 197, 199, 211, 223, 229, 239, 241, 257, 263, 271, 281, 283, 307, 313, 317, 331, 347, 349, 359, 367, 373, 383, 389, 401, 409, 419, 433
Offset: 1

Views

Author

Antti Karttunen, Jun 04 2004

Keywords

Comments

Contains all primes p whose Zeckendorf-expansion A014417(p) ends with an even number of 0's.
For generalizations and conjectures, see A184774.

Links

Crossrefs

Intersection of A000040 & A000201. Complement of A095281 in A000040. Cf. A095080, A095083, A095084, A095290, A184792, A184793, A184794, A184796.

Programs

  • Maple
    R:= NULL: count:= 0:
for n from 1 while count < 100 do
  p:= floor(n*phi);
  if isprime(p) then R:= R,p; count:= count+1 fi
od:
R; # Robert Israel, Jan 17 2023
  • Mathematica
    (See A184792.)
  • Python
    from math import isqrt
from itertools import count, islice
from sympy import isprime
def A095280_gen(): # generator of terms
    return filter(isprime,((n+isqrt(5*n**2)>>1) for n in count(1)))
A095280_list = list(islice(A095280_gen(),30)) # Chai Wah Wu, Aug 16 2022

A184864 Numbers m such that prime(m) is of the form floor(n+nr-r/2), where r=(1+sqrt(5))/2; complement of A184861.

Original entry on oeis.org

4, 7, 13, 14, 17, 19, 26, 27, 29, 31, 33, 36, 41, 47, 50, 56, 58, 60, 65, 67, 69, 74, 77, 78, 83, 84, 85, 87, 88, 91, 94, 95, 97, 100, 104, 106, 108, 110, 113, 114, 117, 119, 121, 123, 128, 129, 135, 138, 139, 142, 143, 145, 146, 148, 150, 152, 155, 160, 163, 166, 167, 169, 174, 176, 177, 180, 183, 186, 187, 190, 191, 195, 196, 198, 201, 203, 207, 209, 211, 216, 220, 221, 222, 224, 227, 228, 235, 239, 243, 244, 246, 247
Offset: 1

Views

Author

Clark Kimberling, Jan 23 2011

Keywords

Crossrefs

Cf. A184774, A184862, A184863.

Programs

  • Mathematica
    r=(1+5^(1/2))/2;
a[n_]:=Floor [n+n*r-r/2];
Table[a[n], {n, 1, 120}]  (* A007064 *)
t1={}; Do[If[PrimeQ[a[n]], AppendTo[t1, a[n]]], {n, 1, 600}]; t1
t2={}; Do[If[PrimeQ[a[n]], AppendTo[t2, n]], {n, 1, 600}]; t2
t3={}; Do[If[MemberQ[t1, Prime[n]], AppendTo[t3, n]], {n, 1, 300}]; t3
*( Lists t1, t2, t3 match A184862, A184863, A184864.)

A184868 Primes of the form floor((k-1/2)*(2+sqrt(2))+1/2); i.e., primes in A063957.

Original entry on oeis.org

2, 5, 19, 29, 43, 53, 67, 73, 97, 101, 131, 149, 179, 193, 227, 241, 251, 271, 347, 353, 367, 401, 439, 449, 463, 487, 521, 541, 599, 613, 647, 661, 691, 719, 739, 743, 773, 787, 797, 811, 821, 859, 883, 937, 941, 947, 971, 1009, 1019, 1033, 1087, 1091, 1163, 1193, 1217, 1231, 1279, 1289, 1303, 1361, 1367, 1381, 1429, 1439, 1453, 1483, 1487, 1511, 1531, 1559, 1579, 1613, 1627, 1637, 1699, 1709, 1733, 1753, 1777, 1787, 1801, 1811, 1873, 1907, 1931, 1951, 1979, 1999
Offset: 1

Views

Author

Clark Kimberling, Jan 23 2011

Keywords

Comments

See "conjecture generalized" at A184774.

Links

Crossrefs

Cf. A184774, A184869, A184870.

Programs

  • Mathematica
    a[n_]:=Floor [(n-1/2)*(2+2^(1/2))+1/2];
Table[a[n],{n,1,120}]  (* A063957 *)
t1={}; Do[If[PrimeQ[a[n]], AppendTo[t1,a[n]]],{n,1,600}];t1
t2={}; Do[If[PrimeQ[a[n]], AppendTo[t2,n]],{n,1,600}];t2
t3={}; Do[If[MemberQ[t1,Prime[n]],AppendTo[t3,n]],{n,1,400}];t3
(* Lists t1, t2, t3 match A184868, A184869, A184870. *)
  • PARI
    lista(nn) = for (k=1, nn, if (isprime(p=floor((k-1/2)*(2+sqrt(2))+1/2)), print1(p, ", "))); \\ Michel Marcus, Jan 30 2018

A184793 Numbers m such that prime(m) is of the form floor(k*r), where r=(1+sqrt(5))/2; complement of A180736.

Original entry on oeis.org

2, 5, 7, 8, 10, 12, 14, 16, 17, 18, 19, 20, 22, 25, 26, 27, 30, 31, 32, 33, 34, 38, 40, 41, 42, 45, 46, 47, 48, 50, 52, 53, 55, 56, 58, 60, 61, 63, 65, 66, 67, 69, 70, 72, 73, 74, 76, 77, 79, 80, 81, 84, 86, 87, 88, 89, 91, 93, 94, 95, 96, 97, 98, 103, 104, 105, 106, 107, 108, 110, 112, 114, 115, 117, 118, 119, 121, 122, 123, 131, 134, 137, 138, 139, 140, 142, 143, 146, 148, 149, 152, 153, 155, 157, 160, 162, 163
Offset: 1

Views

Author

Clark Kimberling, Jan 22 2011

Keywords

Examples

			See A184792.

Crossrefs

Cf. A184774, A184792, A184795.

Programs

A184795 Numbers m such that prime(m) is of the form floor(k*s), where s=(3+sqrt(5))/2; complement of A184793.

Original entry on oeis.org

1, 3, 4, 6, 9, 11, 13, 15, 21, 23, 24, 28, 29, 35, 36, 37, 39, 43, 44, 49, 51, 54, 57, 59, 62, 64, 68, 71, 75, 78, 82, 83, 85, 90, 92, 99, 100, 101, 102, 109, 111, 113, 116, 120, 124, 125, 126, 127, 128, 129, 130, 132, 133, 135, 136, 141, 144, 145, 147, 150, 151, 154, 156, 158, 159, 161, 164, 168, 170, 172, 173, 175
Offset: 1

Views

Author

Clark Kimberling, Jan 22 2011

Keywords

Comments

Indices of primes that appear in the Beatty sequence A001950, the Beatty sequence of A104457. - R. J. Mathar, Jan 22 2011

Examples

			Prime(1)=2 with k=1. Prime(3)=5 with k=2. Prime(4)=7 with k=3.

Crossrefs

Cf. A184774, A184792, A184793.

Programs

A184862 Primes of the form floor(n+nr-r/2), where r=(1+sqrt(5))/2.

Original entry on oeis.org

7, 17, 41, 43, 59, 67, 101, 103, 109, 127, 137, 151, 179, 211, 229, 263, 271, 281, 313, 331, 347, 373, 389, 397, 431, 433, 439, 449, 457, 467, 491, 499, 509, 541, 569, 577, 593, 601, 617, 619, 643, 653, 661, 677, 719, 727, 761, 787, 797, 821, 823, 829, 839, 857, 863, 881, 907, 941, 967, 983, 991, 1009, 1033, 1049, 1051, 1069, 1093, 1109, 1117, 1151, 1153, 1187, 1193, 1213, 1229, 1237, 1279, 1289, 1297, 1321, 1373, 1381, 1399, 1423, 1433, 1439, 1483, 1499, 1543, 1549, 1559, 1567
Offset: 1

Views

Author

Clark Kimberling, Jan 23 2011

Keywords

Comments

See "conjecture generalized" at A184774.

Crossrefs

Cf. A007064, A184774, A184859, A184863, A184864.

Programs

  • Mathematica
    r=(1+5^(1/2))/2;
a[n_]:=Floor [n+n*r-r/2];
Table[a[n],{n,1,120}]  (* A007064 *)
t1={}; Do[If[PrimeQ[a[n]], AppendTo[t1,a[n]]],{n,1,600}];t1
t2={}; Do[If[PrimeQ[a[n]], AppendTo[t2,n]],{n,1,600}];t2
t3={}; Do[If[MemberQ[t1,Prime[n]],AppendTo[t3,n]],{n,1,300}];t3
*( Lists t1, t2, t3 match A184862, A184863, A184864.)
With[{gr=GoldenRatio},Select[Table[Floor[n+n*gr-gr/2],{n,2000}],PrimeQ]] (* Harvey P. Dale, Sep 18 2024 *)

A184865 Primes of the form floor(nr+h), where r=sqrt(2), h=1/2.

Original entry on oeis.org

3, 7, 11, 13, 17, 23, 31, 37, 41, 47, 59, 61, 71, 79, 83, 89, 103, 107, 109, 113, 127, 137, 139, 151, 157, 163, 167, 173, 181, 191, 197, 199, 211, 223, 229, 233, 239, 257, 263, 269, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 349, 359, 373, 379, 383, 389, 397, 409, 419, 421, 431, 433, 443, 457, 461, 467, 479, 491, 499, 503, 509, 523, 547, 557, 563, 569, 571, 577, 587, 593, 601, 607, 617, 619, 631, 641, 643, 653, 659, 673, 677, 683, 701, 709, 727, 733, 751, 757, 761, 769, 809, 823, 827, 829, 839
Offset: 1

Views

Author

Clark Kimberling, Jan 23 2011

Keywords

Comments

See "conjecture generalized" at A184774.

Links

Crossrefs

Cf. A184774, A184866, A184867, A184868.

Programs

  • Mathematica
    r=2^(1/2); h=1/2; a[n_]:=Floor[n*r+h];
Table[a[n],{n,1,120}] (* A022846, int. nearest 2^(1/2) *)
t1={}; Do[If[PrimeQ[a[n]], AppendTo[t1,a[n]]],{n,1,600}];t1
t2={}; Do[If[PrimeQ[a[n]], AppendTo[t2,n]],{n,1,600}];t2
t3={}; Do[If[MemberQ[t1,Prime[n]],AppendTo[t3,n]],{n,1,300}];t3
(* Lists t1, t2, t3 match A184865, A184866, A184867. *)
Select[Floor[Sqrt[2]Range[1000]+1/2],PrimeQ] (* Harvey P. Dale, Oct 31 2011 *)
  • PARI
    lista(nn) = for (k=1, nn, if (isprime(p=floor(1/2+k*sqrt(2))), print1(p, ", "))); \\ Michel Marcus, Jan 30 2018

A184869 Numbers k such that floor[(k-1/2)*(2+2^(1/2))+1/2] is prime.

Original entry on oeis.org

1, 2, 6, 9, 13, 16, 20, 22, 29, 30, 39, 44, 53, 57, 67, 71, 74, 80, 102, 104, 108, 118, 129, 132, 136, 143, 153, 159, 176, 180, 190, 194, 203, 211, 217, 218, 227, 231, 234, 238, 241, 252, 259, 275, 276, 278, 285, 296, 299, 303, 319, 320, 341, 350, 357, 361, 375, 378, 382, 399, 401, 405, 419, 422, 426, 435, 436, 443, 449, 457, 463, 473, 477, 480, 498, 501, 508, 514, 521, 524, 528, 531, 549, 559, 566, 572, 580, 586
Offset: 1

Views

Author

Clark Kimberling, Jan 23 2011

Keywords

Links

Crossrefs

Cf. A184774, A184868, A184870.

Programs

  • Mathematica
    a[n_]:=Floor[(n-1/2)*(2+2^(1/2))+1/2];
Table[a[n],{n,1,120}]  (* A063957 *)
t1={}; Do[If[PrimeQ[a[n]], AppendTo[t1,a[n]]],{n,1,600}];t1
t2={}; Do[If[PrimeQ[a[n]], AppendTo[t2,n]],{n,1,600}];t2
t3={}; Do[If[MemberQ[t1,Prime[n]],AppendTo[t3,n]],{n,1,400}];t3
(* Lists t1, t2, t3 match A184868, A184869, A184870. *)
  • PARI
    isok(k) = isprime(floor((k-1/2)*(2+sqrt(2))+1/2)); \\ Michel Marcus, Jan 30 2018

A184794 Numbers k such that floor(k*s) is prime, where s = (3 + sqrt(5))/2.

Original entry on oeis.org

1, 2, 3, 5, 9, 12, 16, 18, 28, 32, 34, 41, 42, 57, 58, 60, 64, 73, 74, 87, 89, 96, 103, 106, 112, 119, 129, 135, 145, 152, 161, 165, 168, 177, 183, 200, 207, 209, 213, 229, 232, 236, 245, 252, 261, 264, 268, 271, 275, 278, 280, 284, 287, 291, 294, 310, 316, 317, 326, 330, 335, 339, 348, 355, 358, 362, 371, 381, 387, 390, 394, 397, 401, 417, 427, 429, 440, 456, 459, 465, 481, 488, 497, 498, 504, 507, 520, 546, 550, 553, 555, 562, 566, 568, 569, 582, 585, 592
Offset: 1

Views

Author

Clark Kimberling, Jan 22 2011

Keywords

Examples

			See A184792.

Crossrefs

Cf. A184774, A184792, A184795.

Programs

A184805 Primes of the form floor(k*s), where s=(5+sqrt(5))/4.

Original entry on oeis.org

3, 5, 7, 19, 23, 37, 41, 43, 47, 59, 61, 79, 83, 97, 101, 103, 113, 137, 139, 151, 157, 173, 179, 191, 193, 197, 211, 227, 229, 233, 251, 269, 271, 293, 307, 311, 331, 347, 349, 359, 367, 379, 383, 397, 401, 419, 421, 439, 443, 457, 461, 463, 479, 499, 557, 569, 571, 577, 587, 593, 607, 613, 631, 647, 653, 683, 691, 701, 709, 719, 727, 739, 743, 757, 761, 797, 821, 823, 839, 853, 857, 859, 877, 911, 929, 937, 947, 953, 967, 971, 991, 1009, 1013, 1031, 1049, 1051, 1061, 1063, 1069
Offset: 1

Views

Author

Clark Kimberling, Jan 22 2011

Keywords

Examples

			See A184802.

Crossrefs

Cf. A184774, A108598, A184802, A184806, A184807.

Programs

  • Mathematica
    (See A184802.)
With[{s=(5+Sqrt[5])/4},Select[Table[Floor[s*n],{n,600}],PrimeQ]] (* Harvey P. Dale, Feb 04 2015 *)
Previous Showing 11-20 of 20 results.

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