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 1-8 of 8 results.

A105760 Nonnegative numbers k such that 2k+7 is prime.

Original entry on oeis.org

0, 2, 3, 5, 6, 8, 11, 12, 15, 17, 18, 20, 23, 26, 27, 30, 32, 33, 36, 38, 41, 45, 47, 48, 50, 51, 53, 60, 62, 65, 66, 71, 72, 75, 78, 80, 83, 86, 87, 92, 93, 95, 96, 102, 108, 110, 111, 113, 116, 117, 122, 125, 128, 131, 132, 135, 137, 138, 143, 150, 152, 153, 155, 162
Offset: 1

Views

Author

Parthasarathy Nambi, May 04 2005

Keywords

Examples

			If n=0, then 2*0 + 7 = 7 (prime).
If n=15, then 2*15 + 7 = 37 (prime).
If n=27, then 2*27 + 7 = 61 (prime).

Links

Crossrefs

Cf. A153053 (Numbers n such that 2n+7 is not a prime)
Numbers n such that 2n+k is prime: A005097 (k=1), A067076 (k=3), A089038 (k=5), this seq(k=7), A155722 (k=9), A101448 (k=11), A153081 (k=13), A089559 (k=15), A173059 (k=17), A153143 (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

Extensions

More terms from Rick L. Shepherd, May 18 2005

A153144 Numbers n such that 2*n+19 is not a prime.

Original entry on oeis.org

1, 3, 4, 7, 8, 10, 13, 15, 16, 18, 19, 22, 23, 25, 28, 29, 31, 33, 34, 36, 37, 38, 40, 43, 46, 48, 49, 50, 51, 52, 53, 55, 57, 58, 61, 62, 63, 64, 67, 68, 70, 71, 73, 75, 76, 78, 79, 82, 83, 84, 85, 88, 91, 92, 93, 94, 95, 97, 98, 99, 100, 101
Offset: 1

Views

Author

Vincenzo Librandi, Dec 19 2008

Keywords

Links

Crossrefs

Cf. A153143, A153081, A155551.
Numbers n such that 2n+k is not prime: A047845 (k=1), A153238 (k=3), A153052 (k=5), A153053 (k=7), A153723 (k=9), A153083 (k=11), A153082 (k=13), A241571 (k=15), A241572 (k=17), this sequence (k=19).

Programs

  • Magma
    [n: n in [1..120] | not IsPrime(2*n + 19)]; // Vincenzo Librandi, Dec 13 2012
  • Mathematica
    Select[Range[0, 500], !PrimeQ[2# + 19] &] (* Vincenzo Librandi, Dec 13 2012 *)

A153083 Numbers such that 2*n + 11 is not prime.

Original entry on oeis.org

2, 5, 7, 8, 11, 12, 14, 17, 19, 20, 22, 23, 26, 27, 29, 32, 33, 35, 37, 38, 40, 41, 42, 44, 47, 50, 52, 53, 54, 55, 56, 57, 59, 61, 62, 65, 66, 67, 68, 71, 72, 74, 75, 77, 79, 80, 82, 83, 86, 87, 88, 89, 92, 95, 96, 97, 98, 99, 101, 102, 103, 104, 105, 107, 110, 112
Offset: 1

Views

Author

Vincenzo Librandi, Dec 18 2008

Keywords

Comments

One less than the associated entry in A155723. [ R. J. Mathar, Jan 05 2011]

Examples

			Distribution of the terms in the following triangular array:
*
2,7;
5,12,19;
8,17,26,35;
11,22,33,44,55;
14,27,40,53,66,79;
17,32,47,62,77,92,107;
20,37,54,71,88,105,122,139;
23,42,61,80,99,118,137,156,175;
26,47,68,89,110,131,152,173,194,215;
29,52,75,98,121,144,167,190,213,236,259;
32,57,82,107,132,157,182,207,232,257,282,307;
where * marks the decimal values of (2*h*k + k + h - 5) with h >= k >= 1. - _Vincenzo Librandi_, Jan 16 2013

Links

Crossrefs

Cf. A101448, A155546, A155723, A153053.

Programs

  • Magma
    [n: n in [1..120] | not IsPrime(2*n + 11)]; // Vincenzo Librandi, Nov 21 2012
  • Mathematica
    Select[Range[100],!PrimeQ[2#+11]&] (* Harvey P. Dale, Jul 18 2011 *)

A154684 Triangle read by rows where T(m,n)=2mn + m + n - 3, 1<=n<=m.

Original entry on oeis.org

1, 4, 9, 7, 14, 21, 10, 19, 28, 37, 13, 24, 35, 46, 57, 16, 29, 42, 55, 68, 81, 19, 34, 49, 64, 79, 94, 109, 22, 39, 56, 73, 90, 107, 124, 141, 25, 44, 63, 82, 101, 120, 139, 158, 177, 28, 49, 70, 91, 112, 133, 154, 175, 196, 217, 31, 54, 77, 100, 123, 146, 169
Offset: 1

Views

Author

Vincenzo Librandi, Jan 18 2009

Keywords

Comments

2*T(m,n)+7 = (2n+1)*(2m+1) is not prime.
First column: A016777; second column: A016897; third column: A008589; fourth column: A017173. - Vincenzo Librandi, Nov 19 2012

Examples

			Triangle begins:
1;
4,  9;
7,  14, 21;
10, 19, 28, 37;
13, 24, 35, 46, 57;
16, 29, 42, 55, 68,  81;
19, 34, 49, 64, 79,  94,  109;
22, 39, 56, 73, 90,  107, 124, 141;
25, 44, 63, 82, 101, 120, 139, 158, 177;
28, 49, 70, 91, 112, 133, 154, 175, 196, 217; etc.

Links

Crossrefs

Cf. A153053, A105760, A162265 (row sums), A016777, A016897, A008589, A017173.

Programs

  • Magma
    [(2*n*k + n + k - 3): k in [1..n], n in [1..11]]; // Vincenzo Librandi, Nov 19 2012
  • Mathematica
    t[n_,k_]:=2 n*k + n + k - 3; Table[t[n, k], {n, 20}, {k, n}]//Flatten (* Vincenzo Librandi, Nov 19 2012 *)

A155723 Numbers k such that 2*k + 9 is not prime.

Original entry on oeis.org

0, 3, 6, 8, 9, 12, 13, 15, 18, 20, 21, 23, 24, 27, 28, 30, 33, 34, 36, 38, 39, 41, 42, 43, 45, 48, 51, 53, 54, 55, 56, 57, 58, 60, 62, 63, 66, 67, 68, 69, 72, 73, 75, 76, 78, 80, 81, 83, 84, 87, 88, 89, 90, 93, 96, 97, 98, 99, 100, 102, 103, 104, 105, 106, 108, 111, 113, 114
Offset: 1

Views

Author

Vincenzo Librandi, Jan 25 2009

Keywords

Comments

2*A155724(m,n) + 9 = (2n+1)*(2m+1) are not prime and create entries of this form. Also, one less than the associate entry in A153053, two less than the associated A153052. - R. J. Mathar, Jan 05 2011

Examples

			Distribution of the terms in the following triangular array:
   0;
   3,  8;
   6, 13, 20;
   9, 18, 27,  36;
  12, 23, 34,  45,  56;
  15, 28, 41,  54,  67,  80;
  18, 33, 48,  63,  78,  93, 108;
  21, 38, 55,  72,  89, 106, 123, 140;
  24, 43, 62,  81, 100, 119, 138, 157, 176;
  27, 48, 69,  90, 111, 132, 153, 174, 195, 216;
  30, 53, 76,  99, 122, 145, 168, 191, 214, 237, 260;
  33, 58, 83, 108, 133, 158, 183, 208, 233, 258, 283, 308;
  36, 63, 90, 117, 144, 171, 198, 225, 252, 279, 306, 333, 360;
  etc.
the values of (2*h*k + k + h - 4) with h >= k >= 1. - _Vincenzo Librandi_, Jan 16 2013

Links

Crossrefs

Cf. A155724, A155722.

Programs

A301451 Numbers congruent to {1, 7} mod 9.

Original entry on oeis.org

1, 7, 10, 16, 19, 25, 28, 34, 37, 43, 46, 52, 55, 61, 64, 70, 73, 79, 82, 88, 91, 97, 100, 106, 109, 115, 118, 124, 127, 133, 136, 142, 145, 151, 154, 160, 163, 169, 172, 178, 181, 187, 190, 196, 199, 205, 208, 214, 217, 223, 226, 232, 235, 241, 244, 250, 253, 259, 262, 268
Offset: 1

Views

Author

Bruno Berselli, Mar 21 2018

Keywords

Comments

First bisection of A056991, second bisection of A242660.
The squares of the terms of A174396 are the squares of this sequence.

Links

Crossrefs

Cf. A274406: numbers congruent to {0, 8} mod 9.
Cf. A193910: numbers congruent to {2, 6} mod 9.
Subsequence of A016777, A026225, A029739, A033627, A047236, A047259, A055047, A055054, A056991, A153053, A187318, A242660.

Programs

  • GAP
    a := [1,7,10];; for n in [4..60] do a[n] := a[n-1] + a[n-2] - a[n-3]; od; a;
  • Magma
    &cat [[9*n+1, 9*n+7]: n in [0..40]];
  • Mathematica
    Table[2 (2 n - 1) + (2 n - 3 (1 - (-1)^n))/4, {n, 1, 60}]
{#+1,#+7}&/@(9*Range[0,30])//Flatten (* or *) LinearRecurrence[{1,1,-1},{1,7,10},60] (* Harvey P. Dale, Nov 08 2020 *)
  • PARI
    Vec(x*(1 + 6*x + 2*x^2) / ((1 - x)^2*(1 + x)) + O(x^60)) \\ Colin Barker, Mar 22 2018
  • Python
    [2*(2*n-1)+(2*n-3*(1-(-1)**n))/4 for n in range(1,70)]
  • Sage
    [n for n in (1..300) if n % 9 in (1,7)]

Formula

O.g.f.: x*(1 + 6*x + 2*x^2)/((1 + x)*(1 - x)^2).
E.g.f.: (3 + 8*exp(x) - 11*exp(2*x) + 18*x*exp(2*x))*exp(-x)/4.
a(n) = a(n-1) + a(n-2) - a(n-3).
a(n) = 2*(2*n - 1) + (2*n - 3*(1 - (-1)^n))/4. Therefore, for n even a(n) = (9*n - 4)/2, otherwise a(n) = (9*n - 7)/2.
a(2n+1) = A017173(n). a(2n) = A017245(n-1). - R. J. Mathar, Feb 28 2019

A153082 Numbers k such that 2*k + 13 is not prime.

Original entry on oeis.org

1, 4, 6, 7, 10, 11, 13, 16, 18, 19, 21, 22, 25, 26, 28, 31, 32, 34, 36, 37, 39, 40, 41, 43, 46, 49, 51, 52, 53, 54, 55, 56, 58, 60, 61, 64, 65, 66, 67, 70, 71, 73, 74, 76, 78, 79, 81, 82, 85, 86, 87, 88, 91, 94, 95, 96, 97, 98, 100, 101, 102, 103, 104, 106, 109, 111
Offset: 1

Views

Author

Vincenzo Librandi, Dec 18 2008

Keywords

Comments

One less than the associated entry in A153083. - R. J. Mathar, Jan 05 2011

Examples

			Distribution in the following triangular array:
*;
1, 6;
4, 11,18;
7, 16,25,34;
10,21,32,43,54;
13,26,39,52,65,78;
16,31,46,61,76,91,106;
19,36,53,70,87,104,121,138;
22,41,60,79,98,117,136,155,174;
25,46,67,88,109,130,151,172,193,214;
28,51,74,97,120,143,166,189,212,235,258;
31,56,81,106,131,156,181,206,231,256,281,306;
34,61,88,115,142,169,196,223,250,277,304,331,358; etc.
where * marks the negative values of (2*h*k + k + h - 6) with h >= k >= 1. -
_Vincenzo Librandi_, Jan 15 2013

Links

Crossrefs

Cf. A153081, A153083, A155550, A153053.

Programs

  • Magma
    [n: n in [1..120] | not IsPrime(2*n + 13)]; // Vincenzo Librandi, Nov 21 2012
  • Mathematica
    Select[Range[0,100],!PrimeQ[2#+13]&]  (* Harvey P. Dale, Mar 17 2011 *)

A153086 Numbers n such that 4*n+7 is not prime.

Original entry on oeis.org

2, 5, 7, 8, 11, 12, 14, 17, 20, 21, 22, 23, 26, 27, 28, 29, 32, 34, 35, 37, 38, 41, 42, 44, 45, 47, 49, 50, 52, 53, 56, 57, 59, 60, 62, 63, 65, 67, 68, 70, 71, 72, 73, 74, 77, 78, 79, 80, 82, 83, 84, 86, 87, 89, 91, 92, 95, 96, 97, 98, 99, 100, 101, 102, 104, 105, 107
Offset: 1

Views

Author

Vincenzo Librandi, Dec 18 2008

Keywords

Examples

			*;
2, *;
*, 7, *;
5, *, 14, *;
*, 12, *, 23, *;
8, *, 21, *, 34, *;
*, 17, *, 32, *, 47, *; etc.
where * marks the non-integer values of (2*n*k + k + n - 3)/2 with n >= k >= 1. - _Vincenzo Librandi_, Nov 21 2012

Links

Crossrefs

Cf. A089986, A153053.

Programs

  • Magma
    [n: n in [1..120] | not IsPrime(4*n + 7)]; // Vincenzo Librandi, Nov 21 2012
  • Mathematica
    Select[Range[200], !PrimeQ[4# + 7] &] (* Vincenzo Librandi, Nov 21 2012 *)
Showing 1-8 of 8 results.

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