A298866 -id:A298866 - cp's OEIS frontend

A298865 The primes p and products 4*p in increasing order.

2, 3, 5, 7, 8, 11, 12, 13, 17, 19, 20, 23, 28, 29, 31, 37, 41, 43, 44, 47, 52, 53, 59, 61, 67, 68, 71, 73, 76, 79, 83, 89, 92, 97, 101, 103, 107, 109, 113, 116, 124, 127, 131, 137, 139, 148, 149, 151, 157, 163, 164, 167, 172, 173, 179, 181, 188, 191, 193

Offset: 1

Clark Kimberling, Feb 13 2018

Conjecture: except for the first term, these are the nonsquares n for which there is a unique pair (x,y) such that x^2 - y^2 = n and x > y >= 0; see A257408.

Clark Kimberling, Table of n, a(n) for n = 1..1000

Cf. A000040, A298866, A298867.

z = 10000; u = Prime[Range[z]]; w = Take[Union[u, 4 u], z]; (* A298865 *)
p[n_] := If[MemberQ[u, w[[n]]], 0, 1];
t = Table[p[n], {n, 1, z}];
Flatten[Position[t, 0]];  (* A298866 *)
Flatten[Position[t, 1]];  (* A298867 *)

A298867 Positions of numbers 4p when all primes p and products 4p are arranged in increasing order.

Original entry on oeis.org

5, 7, 11, 13, 19, 21, 26, 29, 33, 40, 41, 46, 51, 53, 57, 63, 68, 71, 75, 81, 82, 87, 90, 95, 101, 105, 107, 110, 113, 117, 127, 131, 134, 135, 143, 146, 151, 156, 160, 165, 168, 170, 178, 180, 183, 184, 193, 202, 204, 206, 209, 214, 215, 222, 227, 233, 237

Offset: 1

Clark Kimberling, Apr 14 2018

			The joint ranking begins with 2,3,5,7,8,11,12,13,17,19,20, as in A298865, so that ranks occupied by products 4*p are 5,7,11,...

Clark Kimberling, Table of n, a(n) for n = 1..1000

Cf. A000040, A298866, A298866 (complement).

z = 200; u = Prime[Range[z]]; w = Take[Union[u, 4 u], z];  (* A298865 *)
p[n_] := If[MemberQ[u, w[[n]]], 0, 1];
t = Table[p[n], {n, 1, z}];
Flatten[Position[t, 0]]  (* A298866 *)
Flatten[Position[t, 1]]  (* A298867 *)

cp's OEIS Frontend

A298865 The primes p and products 4*p in increasing order.

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A298867 Positions of numbers 4p when all primes p and products 4p are arranged in increasing order.

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Mathematica

cp's OEIS Frontend

A298865 The primes p and products 4*p in increasing order.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A298867 Positions of numbers 4*p when all primes p and products 4*p are arranged in increasing order.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

A298867 Positions of numbers 4p when all primes p and products 4p are arranged in increasing order.