A077038 -id:A077038 - cp's OEIS frontend

A090121 Numbers n such that nextprime(n^3)-prevprime(n^3) = 4.

2, 129, 189, 369, 435, 549, 555, 561, 819, 1245, 1491, 1719, 1779, 1839, 1875, 1935, 2175, 2289, 2415, 2451, 2595, 2709, 2769, 3141, 3441, 4401, 4611, 4851, 5655, 5775, 6075, 6099, 6795, 6969, 7125, 7239, 7365, 8109, 8139, 8325, 8361, 8385, 8535, 8685, 9591

Offset: 1

Labos Elemer, Jan 12 2004

nonn

			n=129:{p=2146687,n^3=2146689,q=2146691}, q-p=4.

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Cf. A077038, A058043, A090122-A090125, A178228.

pre[x_] := Prime[PrimePi[x]] nex[x_] := Prime[PrimePi[x]+1] de[x_] := Prime[PrimePi[x]+1]-Prime[PrimePi[x]] k=3;Do[If[Equal[Prime[PrimePi[n^k]+1]-Prime[PrimePi[n^k]], 4], Print[n]], {n, 2, 100000}]
lst={};Do[m=n^3;If[PrimeQ[m-2]&&PrimeQ[m+2],AppendTo[lst,n]],{n,0,10^5}];lst (* Vladimir Joseph Stephan Orlovsky, Sep 04 2008 *)
Select[Range[2,6100],NextPrime[#^3]-NextPrime[#^3,-1]==4&] (* Harvey P. Dale, Sep 17 2017 *)

is(n)=if(n%2, isprime(n^3-2) && isprime(n^3+2), n==2) \\ Charles R Greathouse IV, Feb 22 2018

Solutions to A077038(x) = 4.

More terms from Harvey P. Dale, Sep 17 2017

A082037 A square array of linear-factorial numbers, read by antidiagonals.

Original entry on oeis.org

1, 1, 1, 1, 2, 2, 1, 3, 6, 6, 1, 4, 10, 24, 24, 1, 5, 14, 42, 120, 120, 1, 6, 18, 60, 216, 720, 720, 1, 7, 22, 78, 312, 1320, 5040, 5040, 1, 8, 26, 96, 408, 1920, 9360, 40320, 40320, 1, 9, 30, 114, 504, 2520, 13680, 75600, 362880, 362880

Offset: 0

Paul Barry, Apr 02 2003

Rows include A000142(n), A000142(n+1), A007680, A082033, A082034. Columns include 2!*A005408(n),3!*A016777(n),4!*A016813(n),5!*A016861. Main diagonal is A082042.

			Rows begin
1 1 2 6 ....
1 2 6 24 ...
1 3 10 42 ...
1 4 14 60 ...
1 5 18 78 ...

Cf. A077038.

Square array defined by T(n, k)=(kn+1)n!

A090122 Numbers k such that nextprime(k^4) - prevprime(k^4) = 4.

Original entry on oeis.org

2, 3, 21, 34, 46, 87, 99, 129, 141, 220, 242, 254, 266, 278, 279, 476, 526, 550, 616, 627, 657, 772, 777, 783, 795, 1072, 1088, 1322, 1442, 1486, 1540, 1552, 1586, 1653, 1725, 1833, 1959, 1994, 2001, 2043, 2068, 2192, 2224, 2360, 2384, 2432, 2734, 2770, 2866

Offset: 1

Labos Elemer, Jan 12 2004

nonn

			For k = 21: k^4 = 194481, q = nextprime(k^4) = 194483, p = prevprime(k^4) = 194479, q - p = 4, so 21 is in the sequence.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A077038, A058043, A090123, A090124, A090125.

pre[x_] := Prime[PrimePi[x]]; nex[x_] := Prime[PrimePi[x]+1]; de[x_] := Prime[PrimePi[x]+1]-Prime[PrimePi[x]]; k=4; Do[If[Equal[Prime[PrimePi[n^k]+1]-Prime[PrimePi[n^k]], 4], Print[n]], {n, 2, 100000}]

is(k) = nextprime(k^4 + 1) - precprime(k^4 - 1) == 4; \\ Amiram Eldar, Jun 09 2024

a(29)-a(49) from Giovanni Resta, May 08 2017

A090123 Integers k such that nextprime(k^5) - prevprime(k^5) = 4.

Original entry on oeis.org

411, 741, 819, 4041, 6165, 6315, 6861, 10281, 11025, 12489, 12579, 13119, 14331, 15225, 16095, 19125, 19881, 19929, 20799, 22461, 24051, 24885, 25815, 25971, 26979, 27075, 29955, 30801, 31641, 32661, 37371, 38361, 39369, 41181, 42681

Offset: 1

Labos Elemer, Jan 12 2004

nonn

			For k = 411, k^5 = 11727599043051; nextprime(k^5) - prevprime(k^5) = 11727599043053 - 11727599043049 = 4, so k is in the sequence.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A077038, A058043, A090121, A090122, A090124, A090125.

pre[x_] := Prime[PrimePi[x]]; nex[x_] := Prime[PrimePi[x]+1]; de[x_] := Prime[PrimePi[x]+1]-Prime[PrimePi[x]]; k=5; Do[If[Equal[Prime[PrimePi[n^k]+1]-Prime[PrimePi[n^k]], 4], Print[n]], {n, 2, 100000}]
np4Q[n_]:=Module[{c=n^5},NextPrime[c]-NextPrime[c,-1]==4]; Select[ Range[ 43000], np4Q] (* Harvey P. Dale, Oct 06 2017 *)

isok(n) = (nextprime(n^5+1) - precprime(n^5-1)) == 4; \\ Michel Marcus, May 25 2018

Wrong term 1 removed by Michel Marcus, May 25 2018

cp's OEIS Frontend

A090121 Numbers n such that nextprime(n^3)-prevprime(n^3) = 4.

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A082037 A square array of linear-factorial numbers, read by antidiagonals.

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A090122 Numbers k such that nextprime(k^4) - prevprime(k^4) = 4.

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Mathematica

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A090123 Integers k such that nextprime(k^5) - prevprime(k^5) = 4.

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Author

Keywords

Examples

Links

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Programs

Mathematica

PARI

Extensions