A153043 -id:A153043 - cp's OEIS frontend

A153039 Numbers k such that 2*k-7 is composite.

8, 11, 14, 16, 17, 20, 21, 23, 26, 28, 29, 31, 32, 35, 36, 38, 41, 42, 44, 46, 47, 49, 50, 51, 53, 56, 59, 61, 62, 63, 64, 65, 66, 68, 70, 71, 74, 75, 76, 77, 80, 81, 83, 84, 86, 88, 89, 91, 92, 95, 96, 97, 98, 101, 104, 105, 106, 107, 108, 110, 111, 112

Offset: 1

Vincenzo Librandi, Dec 17 2008

Two more than the associated value in A153043, one more than in A153040.

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

Complement of A089192, A153040.

[n: n in [5..220]| not IsPrime(2*n-7)];

Select[Range[8,200], !PrimeQ[2*#-7]&] (* Vladimir Joseph Stephan Orlovsky, Feb 09 2012 *)

list(n)=apply(k->(k+7)/2,setminus(vector(n,k,2*k+7), primes(primepi(2*n+7)))) \\ Charles R Greathouse IV, May 14 2012

Partially edited by N. J. A. Sloane, Jun 23 2010

A153040 Numbers n>3 such that 2*n-5 is not a prime.

Original entry on oeis.org

7, 10, 13, 15, 16, 19, 20, 22, 25, 27, 28, 30, 31, 34, 35, 37, 40, 41, 43, 45, 46, 48, 49, 50, 52, 55, 58, 60, 61, 62, 63, 64, 65, 67, 69, 70, 73, 74, 75, 76, 79, 80, 82, 83, 85, 87, 88, 90, 91, 94, 95, 96, 97, 100, 103, 104, 105, 106, 107, 109, 110, 111

Offset: 1

Vincenzo Librandi, Dec 17 2008

One less than the associated number in A153039; one more than that in A153043. - R. J. Mathar Dec 20 2008

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

Cf. A089253, A153039.

[n: n in [4..120]|not IsPrime(2*n-5)]; // Vincenzo Librandi, Aug 30 2012

Select[Range[4,200],!PrimeQ[2*#-5]&] (* Vladimir Joseph Stephan Orlovsky, Feb 09 2012 *)

Let p = prime number n = (p^2+5)/2 mod (p)

Flipped sign in definition. - R. J. Mathar, Dec 20 2008

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

Vincenzo Librandi, Dec 17 2008

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

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

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.

[n: n in [10..150] | not IsPrime(2*n - 19)]; // Vincenzo Librandi, Jan 19 2013

Select[Range[10, 200], !PrimeQ[2 # - 19] &] (* Vincenzo Librandi, Jan 19 2013 *)

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

A153045 Numbers k such that 2*k-11 is not a prime.

Original entry on oeis.org

10, 13, 16, 18, 19, 22, 23, 25, 28, 30, 31, 33, 34, 37, 38, 40, 43, 44, 46, 48, 49, 51, 52, 53, 55, 58, 61, 63, 64, 65, 66, 67, 68, 70, 72, 73, 76, 77, 78, 79, 82, 83, 85, 86, 88, 90, 91, 93, 94, 97, 98, 99, 100, 103, 106, 107, 108, 109, 110, 112, 113, 114

Offset: 1

Vincenzo Librandi, Dec 17 2008

The terms are the values of 2*h*k + k + h + 6, where h and k are positive integers. - Vincenzo Librandi, Jan 19 2013

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

Cf. A097338, A153043, A163652, A104275.

[n: n in [7..120] | not IsPrime(2*n - 11)]; // Vincenzo Librandi, Oct 11 2012

Select[Range[10,200], !PrimeQ[2*#-11]&] (* Vladimir Joseph Stephan Orlovsky, Feb 09 2012 *)

from sympy import isprime
def ok(n): return n > 6 and not isprime(2*n-11)
print(list(filter(ok, range(115)))) # Michael S. Branicky, Oct 13 2021

a(n) = 5+A104275(n+1). [R. J. Mathar, Oct 22 2009]

A153047 Numbers n such that 2*n-15 is not a prime.

Original entry on oeis.org

12, 15, 18, 20, 21, 24, 25, 27, 30, 32, 33, 35, 36, 39, 40, 42, 45, 46, 48, 50, 51, 53, 54, 55, 57, 60, 63, 65, 66, 67, 68, 69, 70, 72, 74, 75, 78, 79, 80, 81, 84, 85, 87, 88, 90, 92, 93, 95, 96, 99, 100, 101, 102, 105, 108, 109, 110, 111, 112, 114, 115, 116

Offset: 1

Vincenzo Librandi, Dec 17 2008

One more than the associated entry in A153049. - R. J. Mathar, Jan 05 2011

The terms are the values of 2*h*k + k + h + 8, where h and k are positive integers.- Vincenzo Librandi, Jan 19 2013

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

Cf. A097480, A153043, A153045, A153049, A163657.

[n: n in [10..120] | not IsPrime(2*n - 15)]; // Vincenzo Librandi, Oct 11 2012

Select[Range[12,200], !PrimeQ[2*#-15]&] (* Vladimir Joseph Stephan Orlovsky, Feb 09 2012 *)

A155705 Triangle read by rows where T(m,n) = 2mn + m + n + 2.

Original entry on oeis.org

6, 9, 14, 12, 19, 26, 15, 24, 33, 42, 18, 29, 40, 51, 62, 21, 34, 47, 60, 73, 86, 24, 39, 54, 69, 84, 99, 114, 27, 44, 61, 78, 95, 112, 129, 146, 30, 49, 68, 87, 106, 125, 144, 163, 182, 33, 54, 75, 96, 117, 138, 159, 180, 201, 222, 36, 59, 82, 105, 128, 151

Offset: 1

Vincenzo Librandi, Jan 25 2009

2*T(m,n)-3 = (2*m+1)*(2*n+1) is not prime, obviously. Also: first column: 3*A020725; second column: A016897; third column: A017041; fourth column: 3*A016789. - Vincenzo Librandi, Nov 20 2012

			Triangle begins:
6;
9,  14;
12, 19, 26;
15, 24, 33, 42;
18, 29, 40, 51, 62;
21, 34, 47, 60, 73,  86;
24, 39, 54, 69, 84,  99,  114;
27, 44, 61, 78, 95,  112, 129, 146;
30, 49, 68, 87, 106, 125, 144, 163, 182;
33, 54, 75, 96, 117, 138, 159, 180, 201, 222; etc.

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

Cf. A153043, A020725, A016897, A017041.

[2*n*k + n + k + 2: k in [1..n],  n in [1..11]]; // Vincenzo Librandi, Nov 20 2012

t[n_,k_]:=2 n*k + n + k + 2; Table[t[n, k], {n, 11}, {k, n}]//Flatten (* Vincenzo Librandi, Nov 20 2012 *)

A345447 Numbers of the form i+j+2ij and 2+i+j+2ij for i,j >= 1.

Original entry on oeis.org

4, 6, 7, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 42, 43, 44, 45, 46, 47, 48, 49, 51, 52, 54, 55, 57, 58, 59, 60, 61, 62, 63, 64, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80

Offset: 1

Davide Rotondo, Jun 19 2021

nonn

Except for 1 and 2 the complement sequence c is: 3, 5, 8, 11, 20, 23, 35, 41, 50, 53, 56, 65, ...; where 2*c(i) + 1 and 2*c(i) - 3 are a pair of cousin primes. This is a consequence of the sieve of Sundaram.

			For i,j = 1, 1+1+2*1*1 = 4 and 2+1+1+2*1*1 = 6.

Wikipedia, Sieve of Sundaram.

Cf. A046132, A023200.

Union of A047845 and A153043, except for 0 and 2.

def aupto(limit):
    aset = set()
    for i in range(1, limit//3):
        for j in range(i, limit//3):
            t = i + j + 2*i*j
            if t > limit: break
            aset.update([t, t+2])
    return sorted(an for an in aset if an <= limit)
print(aupto(80)) # Michael S. Branicky, Jul 05 2021

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A153039 Numbers k such that 2*k-7 is composite.

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A153040 Numbers n>3 such that 2*n-5 is not a prime.

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

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A153045 Numbers k such that 2*k-11 is not a prime.

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A153047 Numbers n such that 2*n-15 is not a prime.

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A155705 Triangle read by rows where T(m,n) = 2*m*n + m + n + 2.

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Magma

Mathematica

A345447 Numbers of the form i+j+2*i*j and 2+i+j+2*i*j for i,j >= 1.

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Python

A155705 Triangle read by rows where T(m,n) = 2mn + m + n + 2.

A345447 Numbers of the form i+j+2ij and 2+i+j+2ij for i,j >= 1.