A184870 -id:A184870 - cp's OEIS frontend

A184867 Numbers m such that prime(m) is of the form floor(1/2+k*sqrt(2)). Complement of A184870.

2, 4, 5, 6, 7, 9, 11, 12, 13, 15, 17, 18, 20, 22, 23, 24, 27, 28, 29, 30, 31, 33, 34, 36, 37, 38, 39, 40, 42, 43, 45, 46, 47, 48, 50, 51, 52, 55, 56, 57, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 83, 84, 86, 88, 89, 91, 92, 94, 95, 96, 97, 99, 101, 102, 103, 104, 105, 106, 107, 108, 110, 111, 113, 114, 115, 116, 117, 119, 120, 122, 123, 124, 126, 127, 129, 130, 133, 134, 135, 136, 140, 143, 144, 145, 146

Offset: 1

Clark Kimberling, Jan 23 2011

nonn

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

Cf. A022846, A184865, A184866, A184870.

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. *)

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

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, A184869, A184870.

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. *)

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

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

Clark Kimberling, Jan 23 2011

nonn

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

Cf. A184774, A184868, A184870.

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. *)

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

cp's OEIS Frontend

A184867 Numbers m such that prime(m) is of the form floor(1/2+k*sqrt(2)). Complement of A184870.

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

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

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Mathematica

PARI