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.

Showing 1-4 of 4 results.

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

Original entry on oeis.org

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

Views

Author

Labos Elemer, Jan 12 2004

Keywords

Examples

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

Links

Crossrefs

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

Programs

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

Formula

Solutions to A077038(x) = 4.

Extensions

More terms from Harvey P. Dale, Sep 17 2017

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

Views

Author

Labos Elemer, Jan 12 2004

Keywords

Examples

			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.

Links

Crossrefs

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

Programs

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

Extensions

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

Views

Author

Labos Elemer, Jan 12 2004

Keywords

Examples

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

Links

Crossrefs

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

Programs

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

Extensions

Wrong term 1 removed by Michel Marcus, May 25 2018

A090124 a(n) is the least positive n-th power integer such that nextprime[a(n)]-prevprime[a(n)]=q-p-4;.

Original entry on oeis.org

5, 4, 8, 16, 11727599043051, 54980371265625, 128, 557556054479199010816, 22027845102081762861, 162889462677744140625, 803596764671634487466709, 14231716419191575233132742871310396257144854491849
Offset: 1

Views

Author

Labos Elemer, Jan 12 2004

Keywords

Examples

			n=4:a(n)=16,{p=13,16=4^4,q=17}

Crossrefs

Cf. A090121-A090125.

Programs

  • Mathematica
    Table[fla=1;Do[If[((PrimeQ[s=n^k-3]&&PrimeQ[s1=n^k+1]) ||(PrimeQ[s=n^k-2]&&PrimeQ[s1=n^k+2])||(PrimeQ[s=n^k-1] &&PrimeQ[s1=n^k+3]))&&Equal[fla, 1]&&!Equal[n, 1], Print[n^k];fla=0], {n, 1, 1000000}], {k, 1, 60}]
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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