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 1-3 of 3 results.

A100419 Numbers k such that 30*k+{1,7,13,17,19,23,29} are all prime.

Original entry on oeis.org

89, 6627, 18674, 223949, 229269, 240007, 267356, 606681, 638454, 771496, 951060, 1068030, 1150693, 1254839, 1688923, 1920084, 2413577, 2433289, 2649414, 3053398, 3080572, 3337444, 3586658, 3604256, 3830335, 4137166
Offset: 1

Views

Author

Ferenc Adorjan (fadorjan(AT)freemail.hu), Nov 19 2004

Keywords

Comments

Values are 5 mod 7.
In each case, the 7 primes are necessarily consecutive. See the comment in A100418. - Peter Munn, Sep 06 2023

Links

Crossrefs

Cf. A005776, A007775, A076205, A100418, A100420-A100423.

Programs

  • Magma
    [ n: n in [5..70000000 by 7] | forall{ q: q in [1, 7, 13, 17, 19, 23, 29] | IsPrime(30*n+q) } ]; // Klaus Brockhaus, Feb 24 2011
  • Maple
    filter:= proc(n) local j; andmap(isprime, [seq(30*n+j,j=[1,7,13,17,19,23,29])]) end proc:
select(filter, [seq(i,i=5..5*10^6,7)]); # Robert Israel, Nov 04 2024
  • Mathematica
    Select[Range[42*10^5],AllTrue[30#+{1,7,13,17,19,23,29},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 10 2018 *)

Extensions

Edited by Don Reble, Nov 17 2005

A100421 Numbers n such that 30*n+{1,7,11,13,19,23,29} are all prime.

Original entry on oeis.org

2, 79, 391701, 505017, 740413, 787187, 933025, 1169863, 1333719, 1406792, 2212261, 2719950, 2962738, 3125992, 3284955, 3384586, 3727271, 3821295, 3861881, 4320864, 4439878, 4764356, 5014865, 5480190, 5879274, 6124442
Offset: 1

Views

Author

Ferenc Adorjan (fadorjan(AT)freemail.hu), Nov 19 2004

Keywords

Comments

Values are 2 mod 7.
In each case, the 7 primes are necessarily consecutive. See the comment in A100418. - Peter Munn, Sep 06 2023

Crossrefs

Cf. A005776, A007775, A076205, A100418-A100420, A100422, A100423.

Programs

  • Magma
    [ n: n in [2..70000000 by 7] | forall{ q: q in [1, 7, 11, 13, 19, 23, 29] | IsPrime(30*n+q) } ]; // Klaus Brockhaus, Feb 24 2011
  • Mathematica
    Select[Range[7*10^6],AllTrue[30#+{1,7,11,13,19,23,29},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 16 2016 *)

Extensions

Edited by Don Reble, Nov 17 2005

A385124 Numbers k such that there are exactly 7 primes between 30*k and 30*k+30.

Original entry on oeis.org

1, 2, 49, 62, 79, 89, 188, 6627, 9491, 18674, 22621, 31982, 34083, 38226, 38520, 41545, 48713, 53887, 89459, 103205, 114731, 123306, 139742, 140609, 149125, 168237, 175125, 210554, 223949, 229269, 237794, 240007, 267356, 288467, 321451, 364921, 368248, 373370, 391701
Offset: 1

Views

Author

Jianglin Luo, Jun 18 2025

Keywords

Comments

The count of primes in 30*k..30*k+30 is less than 8 for k >= 1.
It appears that this sequence has infinitely many terms.

Examples

			1 is a term since there are 7 primes in 30..60: 31, 37, 41, 43, 47, 53, 59.
2 is a term since there are 7 primes in 60..90: 61, 67, 71, 73, 79, 83, 89.
3 is not a term since there are only 6 primes in 90..120: 97, 101, 103, 107, 109, 113.
49 is a term since there are 7 primes in 30*49..30*50: 1471, 1481, 1483, 1487, 1489, 1493, 1499.

Links

Crossrefs

Union of A100418, A100419, A100420, A100421, A100422 and A100423.
Cf. A000720, A098592.

Programs

  • Mathematica
    ArrayPlot[Table[Boole@PrimeQ[i*30+j],{i,0,399},{j,30}],Mesh->True]
index=1;Do[If[Length@(*PrimeRange=*) Select[Range[30*k+1,30*k+30,2],PrimeQ]==7,Print[index++," ",k]],{k,1,10^9}]
  • PARI
    [n|n<-[1..10^6],#primes([30*n,30*n+30])==7]

Formula

{k | A098592(k) = pi(30*k+30) - pi(30*k) = 7}. - Michael S. Branicky, Jun 24 2025
Showing 1-3 of 3 results.

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