A184867 -id:A184867 - cp's OEIS frontend

A184870 Numbers m such that prime(m) is of the form floor[(k-1/2)*(2+2^(1/2))+1/2]; complement of A184867.

1, 3, 8, 10, 14, 16, 19, 21, 25, 26, 32, 35, 41, 44, 49, 53, 54, 58, 69, 71, 73, 79, 85, 87, 90, 93, 98, 100, 109, 112, 118, 121, 125, 128, 131, 132, 137, 138, 139, 141, 142, 149, 153, 159, 160, 161, 164, 169, 171, 174, 181, 182, 192, 196, 199, 202, 207, 209, 213, 218, 219, 221, 226, 228, 231, 235, 236, 240, 242, 246, 249, 255, 258, 259, 266, 267, 270, 273, 275, 277, 279, 280, 287, 292, 294, 297, 299, 303

Offset: 1

Clark Kimberling, Jan 23 2011

nonn

G. C. Greubel, Table of n, a(n) for n = 1..10000

Cf. A063957, A184868, A184869.

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. *)

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

Clark Kimberling, Jan 23 2011

nonn

See "conjecture generalized" at A184774.

G. C. Greubel, Table of n, a(n) for n = 1..10000

Cf. A184774, A184866, A184867, A184868.

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 *)

lista(nn) = for (k=1, nn, if (isprime(p=floor(1/2+k*sqrt(2))), print1(p, ", "))); \\ Michel Marcus, Jan 30 2018

A184866 Numbers k such that floor(1/2+k*sqrt(2)) is prime.

Original entry on oeis.org

2, 5, 8, 9, 12, 16, 22, 26, 29, 33, 42, 43, 50, 56, 59, 63, 73, 76, 77, 80, 90, 97, 98, 107, 111, 115, 118, 122, 128, 135, 139, 141, 149, 158, 162, 165, 169, 182, 186, 190, 196, 199, 200, 207, 217, 220, 221, 224, 234, 238, 247, 254, 264, 268, 271, 275, 281, 289, 296, 298, 305, 306, 313, 323, 326, 330, 339, 347, 353, 356, 360, 370, 387, 394, 398, 402, 404, 408, 415, 419, 425, 429, 436, 438, 446, 453, 455, 462, 466, 476, 479, 483, 496, 501, 514, 518, 531, 535, 538, 544, 572, 582, 585, 586, 593

Offset: 1

Clark Kimberling, Jan 23 2011

nonn

G. C. Greubel, Table of n, a(n) for n = 1..10000

Cf. A184865, A184867.

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. *)

isok(k) = isprime(floor(1/2+k*sqrt(2))); \\ Michel Marcus, Jan 30 2018

cp's OEIS Frontend

A184870 Numbers m such that prime(m) is of the form floor[(k-1/2)*(2+2^(1/2))+1/2]; complement of A184867.

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

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A184866 Numbers k such that floor(1/2+k*sqrt(2)) is prime.

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