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 1-5 of 5 results.

A153143 Nonnegative numbers k such that 2k + 19 is prime.

Original entry on oeis.org

0, 2, 5, 6, 9, 11, 12, 14, 17, 20, 21, 24, 26, 27, 30, 32, 35, 39, 41, 42, 44, 45, 47, 54, 56, 59, 60, 65, 66, 69, 72, 74, 77, 80, 81, 86, 87, 89, 90, 96, 102, 104, 105, 107, 110, 111, 116, 119, 122, 125, 126, 129, 131, 132, 137, 144, 146, 147, 149, 156, 159, 164, 165
Offset: 1

Views

Author

Vincenzo Librandi, Dec 19 2008

Keywords

Comments

Or, (p-19)/2 for primes p >= 19.
a(n) = (A000040(n+7) - 19)/2.
a(n) = A005097(n+6) - 9.
a(n) = A067076(n+6) - 8.
a(n) = A089038(n+5) - 7.
a(n) = A105760(n+4) - 6.
a(n) = A101448(n+3) - 4.
a(n) = A089559(n+1) - 2.

Examples

			For k = 4, 2*k+19 = 27 is not prime, so 4 is not in the sequence;
for k = 17, 2*k+19 = 53 is prime, so 17 is in the sequence.

Links

Crossrefs

Cf. A000040 (prime numbers), A153144 (2n+19 is not prime).
Numbers n such that 2n+k is prime: A005097 (k=1), A067076 (k=3), A089038 (k=5), A105760 (k=7), A155722 (k=9), A101448 (k=11), A153081 (k=13), A089559 (k=15), A173059 (k=17), this seq (k=19).
Numbers n such that 2n-k is prime: A006254 (k=1), A098090 (k=3), A089253 (k=5), A089192 (k=7), A097069 (k=9), A097338 (k=11), A097363 (k=13), A097480 (k=15), A098605 (k=17), A097932 (k=19).

Programs

Formula

a(n) ~ (n/2) log n. - Charles R Greathouse IV, Jan 03 2025

Extensions

Edited, corrected and extended by Klaus Brockhaus, Dec 22 2008
Definition clarified by Zak Seidov, Jul 11 2014

A153041 Numbers n >=10 such that 2*n-19 is not a prime.

Original entry on oeis.org

10, 14, 17, 20, 22, 23, 26, 27, 29, 32, 34, 35, 37, 38, 41, 42, 44, 47, 48, 50, 52, 53, 55, 56, 57, 59, 62, 65, 67, 68, 69, 70, 71, 72, 74, 76, 77, 80, 81, 82, 83, 86, 87, 89, 90, 92, 94, 95, 97, 98, 101, 102, 103, 104
Offset: 1

Views

Author

Vincenzo Librandi, Dec 17 2008

Keywords

Comments

One more than associated values in A153051, two more than A153047. - R. J. Mathar, Jan 05 2011
The terms after a(1) are the values of 2*h*k + k + h + 10, where h and k are positive integers.- Vincenzo Librandi, Jan 19 2013

Links

Crossrefs

Cf. A097932, A155704.
Numbers n such that 2n-k is not prime: A104275 (k=1), A153043 (k=3), A153040 (k=5), A153039 (k=7), A153044 (k=9), A153045 (k=11), A153049 (k=13), A153047 (k=15), A153051 (k=17), A153041 (k=19).
Similar sequence listed also in A089559, A153144.

Programs

  • Magma
    [n: n in [10..150] | not IsPrime(2*n - 19)]; // Vincenzo Librandi, Jan 19 2013
  • Mathematica
    Select[Range[10, 200], !PrimeQ[2 # - 19] &] (* Vincenzo Librandi, Jan 19 2013 *)

Extensions

Edited by N. J. A. Sloane, Jun 22 2010

A155551 Triangle read by rows where T(m,n)=2*m*n + m + n - 9.

Original entry on oeis.org

-5, -2, 3, 1, 8, 15, 4, 13, 22, 31, 7, 18, 29, 40, 51, 10, 23, 36, 49, 62, 75, 13, 28, 43, 58, 73, 88, 103, 16, 33, 50, 67, 84, 101, 118, 135, 19, 38, 57, 76, 95, 114, 133, 152, 171, 22, 43, 64, 85, 106, 127, 148, 169, 190, 211, 25, 48, 71, 94, 117, 140, 163, 186, 209
Offset: 1

Views

Author

Vincenzo Librandi, Jan 24 2009

Keywords

Comments

The numbers 2*T(m,n)+19 =(2*n+1)*(2*m+1) are not prime.
First column: A016777, second column: A016885, third column: A016993, fourth column: A017209. - Vincenzo Librandi, Nov 20 2012

Examples

			Triangle begins:
-5;
-2, 3;
1,  8,  15;
4,  13, 22, 31;
7,  18, 29, 40, 51;
10, 23, 36, 49, 62,  75;
13, 28, 43, 58, 73,  88,  103;
16, 33, 50, 67, 84,  101, 118, 135;
19, 38, 57, 76, 95,  114, 133, 152, 171;
22, 43, 64, 85, 106, 127, 148, 169, 190, 211; etc.

Links

Crossrefs

Cf. A153143, A153144, A016777, A016885, A016993, A017209.

Programs

  • Magma
    [2*n*k + n + k - 9: k in [1..n], n in [1..11]]; // Vincenzo Librandi, Nov 20 2012
  • Mathematica
    t[n_,k_]:=2 n*k + n + k - 9; Table[t[n, k], {n, 15}, {k, n}]//Flatten (* Vincenzo Librandi, Nov 20 2012 *)

A241571 Numbers n such that 2*n+15 is not a prime.

Original entry on oeis.org

0, 3, 5, 6, 9, 10, 12, 15, 17, 18, 20, 21, 24, 25, 27, 30, 31, 33, 35, 36, 38, 39, 40, 42, 45, 48, 50, 51, 52, 53, 54, 55, 57, 59, 60, 63, 64, 65, 66, 69, 70, 72, 73, 75, 77, 78, 80, 81, 84, 85, 86, 87, 90, 93, 94, 95, 96, 97, 99, 100, 101, 102, 103, 105, 108
Offset: 1

Views

Author

Vincenzo Librandi, Apr 27 2014

Keywords

Links

Crossrefs

Complement of A089559.
Cf. similar sequence listed in A153144.

Programs

  • Magma
    [n: n in [0..200] | not IsPrime(2*n+15)];
  • Mathematica
    Select[Range[0, 200], !PrimeQ[2 # + 15] &]

A241572 Numbers n such that 2*n+17 is not a prime.

Original entry on oeis.org

2, 4, 5, 8, 9, 11, 14, 16, 17, 19, 20, 23, 24, 26, 29, 30, 32, 34, 35, 37, 38, 39, 41, 44, 47, 49, 50, 51, 52, 53, 54, 56, 58, 59, 62, 63, 64, 65, 68, 69, 71, 72, 74, 76, 77, 79, 80, 83, 84, 85, 86, 89, 92, 93, 94, 95, 96, 98, 99, 100, 101, 102, 104, 107, 109
Offset: 1

Views

Author

Vincenzo Librandi, Apr 27 2014

Keywords

Links

Crossrefs

Complement of A173059.
Cf. similar sequence listed in A153144.

Programs

  • Magma
    [n: n in [0..200] | not IsPrime(2*n+17)];
  • Mathematica
    Select[Range[0, 200], ! PrimeQ[2 # + 17] &]
Showing 1-5 of 5 results.

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

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