A140869 -id:A140869 - cp's OEIS frontend

A153085 Numbers k such that 4*k + 5 is not prime.

1, 4, 5, 7, 10, 11, 13, 15, 16, 18, 19, 20, 22, 25, 28, 29, 30, 31, 32, 34, 35, 37, 39, 40, 41, 43, 45, 46, 49, 50, 51, 52, 53, 54, 55, 58, 60, 61, 62, 64, 65, 67, 70, 71, 73, 74, 75, 76, 79, 80, 81, 82, 84, 85, 88, 89, 90, 91, 93, 94, 95, 97, 100, 102, 103, 105, 106

Offset: 1

Vincenzo Librandi, Dec 18 2008

nonn

Let p=2n+1 be an odd number, then A140869(n,n) = (p^2-5)/4 = A028387(n-1).

One less than the associated entry in A045751: a(n) = A045751(n+1)-1. - R. J. Mathar, Jan 05 2011

			Triangle begins:
1;
*, 5;
4, *, 11;
*, 10, *, 19;
7, *, 18, *, 29;
*, 15, *, 28, *, 41;
where * mark the entries in A140869 which are non-integer if floor(.) is not applied there.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A028387, A045751, A111215, A140869.

[n: n in [1..120] | not IsPrime(4*n + 5)]; // Vincenzo Librandi, Oct 15 2012

Select[Range[200], !PrimeQ[4 # + 5] &] (* Vincenzo Librandi, Oct 15 2012 *)

A144652 Triangle, read by rows, where T(m,n) = floor((2mn+m+n)/2) with m >= n >= 1.

Original entry on oeis.org

2, 3, 6, 5, 8, 12, 6, 11, 15, 20, 8, 13, 19, 24, 30, 9, 16, 22, 29, 35, 42, 11, 18, 26, 33, 41, 48, 56, 12, 21, 29, 38, 46, 55, 63, 72, 14, 23, 33, 42, 52, 61, 71, 80, 90, 15, 26, 36, 47, 57, 68, 78, 89, 99, 110, 17, 28, 40, 51, 63, 74, 86, 97, 109, 120, 132, 18, 31, 43, 56, 68

Offset: 1

Vincenzo Librandi, Jan 27 2009

From Vincenzo Librandi, Nov 16 2012: (Start)
First column:  A007494(n+1);
second column: A047219(n+2);
third column:  A047383(n+3);
fourth column: A193910(n+4).
Conjecture: If h does not belong to the sequence, then 4*h+1 is prime. (End)

			Triangle begins:
2;
3,  6;
5,  8,  12;
6,  11, 15, 20;
8,  13, 19, 24, 30;
9,  16, 22, 29, 35, 42;
11, 18, 26, 33, 41, 48, 56; etc.

Vincenzo Librandi, Rows n = 1..100, flattened

Cf. A007494, A047219, A047383, A193910.

[Floor((2*n*k+n+k)/2): k in [1..n], n in [1..11]]; // Vincenzo Librandi, Nov 16 2012

Flatten[Table[Floor[(2*n*m + m + n)/2], {n, 1, 20}, {m, n}]] (* Vincenzo Librandi, Nov 16 2012 *)

Definition edited (specifying m >= n >= 1), and terms recomputed to match definition, as was done with the similar sequence A140869, by Jon E. Schoenfield, Jun 24 2010

cp's OEIS Frontend

A153085 Numbers k such that 4*k + 5 is not prime.

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