A120876 -id:A120876 - cp's OEIS frontend

A086870 Primes equal to a product of twin primes minus 1 divided by 2.

7, 17, 71, 449, 881, 2591, 9521, 39761, 106721, 179999, 206081, 342791, 388961, 596231, 847601, 1292831, 2268449, 2571911, 2836961, 3612671, 6223391, 6329681, 6415361, 8520191, 8946449, 9409121, 10342151, 12550049, 16485281, 18800711

Offset: 1

Cino Hilliard, Aug 20 2003

From Jason Kimberley, Oct 22 2015 (Start)
Prime elements of A120876.
For each p in this list, A001221(2p) = A001222(2p) = A001221(2p+1) = A001222(2p+1) = 2.
2*a(n) is a subsequence of A103533. They first differ when 313619 is not in this sequence, but 2*313619 = 627238 = A103533(12).
(End)

			t1 = 71,t2 = 73, (71*73-1)/2 = 5182/2 = 2591 = prime.

Jason Kimberley, Table of n, a(n) for n = 1..10000

Cf. A103533, A120876.

Select[(Times[#, # + 2] - 1)/2 &@ Select[Prime@ Range@ 1000, PrimeQ[# + 2] &], PrimeQ] (* Michael De Vlieger, Nov 06 2015 *)

for(n=1, 1e3, if(prime(n+1)-prime(n)==2 && isprime(k=(prime(n)*prime(n+1)-1)/2), print1(k", "))) \\ Altug Alkan, Nov 06 2015

Primes of the form (t1*t2-1)/2, where t1, t2 are twin primes.

A102770 (p*q - 1)/2 where p and q are consecutive odd primes.

Original entry on oeis.org

7, 17, 38, 71, 110, 161, 218, 333, 449, 573, 758, 881, 1010, 1245, 1563, 1799, 2043, 2378, 2591, 2883, 3278, 3693, 4316, 4898, 5201, 5510, 5831, 6158, 7175, 8318, 8973, 9521, 10355, 11249, 11853, 12795, 13610, 14445, 15483, 16199, 17285, 18431, 19010

Offset: 1

W. Neville Holmes, Feb 10 2005

Primes in this sequence: 7, 17, 71, 449, 881, 2591, ... - Zak Seidov, Jan 14 2013

			a(1) = (3*5 - 1)/2 = 7.
a(2) = (5*7 - 1)/2 = 17.
a(3) = (7*11 - 1)/2 = 38.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A006094, A023515, A086870, A120876.

Table[(Prime[n] Prime[n + 1] - 1)/2, {n, 2, 50}] (* Alonso del Arte, Jan 14 2013 *)
(Times@@#-1)/2&/@Partition[Prime[Range[2,50]],2,1] (* Harvey P. Dale, Apr 10 2015 *)

a(n)=prime(n+1)*prime(n+2)\2 \\ Charles R Greathouse IV, Jan 14 2013

a(n) = (prime(n + 1)*prime(n + 2) - 1)/2.
a(n) ~ 0.5 n^2/log^2 n. - Charles R Greathouse IV, Jan 14 2013
a(n) = A023515(n+2)/2. - Jason Kimberley, Oct 23 2015

A120875 Product of twin primes minus 1.

Original entry on oeis.org

14, 34, 142, 322, 898, 1762, 3598, 5182, 10402, 11662, 19042, 22498, 32398, 36862, 39202, 51982, 57598, 72898, 79522, 97342, 121102, 176398, 186622, 213442, 272482, 324898, 359998, 381922, 412162, 435598, 656098, 675682, 685582, 736162

Offset: 1

Lekraj Beedassy, Jul 09 2006

nonn

This sequence is a subsequence of A023515.

Jason Kimberley (using T. Noe's b037074), Table of n, a(n) for n = 1..10000

Cf. A002822, A023515, A037074, A075369, A120876.

Times[#, # + 2] - 1 & /@ Select[Prime@ Range@ 150, PrimeQ[# + 2] &] (* Michael De Vlieger, Oct 23 2015 *)

for(n=1, 200, if(prime(n+1)-prime(n)==2, print1(prime(n)*prime(n+1)-1", "))) \\ Altug Alkan, Oct 23 2015

a(n) = A037074(n)-1 = (A014574(n))^2 -2 = A075369(n)-2.
a(n) = 2*A120876(n). - Jason Kimberley, Oct 23 2015
a(n) = 36*A002822(n-1)^2-2, for n>1. - Jason Kimberley, Oct 23 2015
a(n) = A023515(A107770(n)). - Jason Kimberley, Oct 23 2015

A094949 Phi(m)*sigma(m), where m is the product of exactly two primes that differ by 2, where phi=A000010, sigma=A000203.

Original entry on oeis.org

192, 1152, 20160, 103680, 806400, 3104640, 12945600, 26853120, 108201600, 136002240, 362597760, 506160000, 1049630400, 1358807040, 1536796800, 2702128320, 3317529600, 5314118400, 6323748480, 9475464960, 14665694400

Offset: 1

Lekraj Beedassy, Jun 19 2004

nonn

If m=p*q for the twin prime pair (p, q), then the relation p^2 + q^2 = 2*(m+2) is evident from equations p*(p+2)=m=q*(q-2). Now phi(m)=(p-1)*(q-1)=p^2 - 1 and sigma(m)=(p+1)*(q+1)=q^2 - 1, so that phi(m)*sigma(m)=(p*q)^2 -(p^2 + q^2)+1=m^2-2*(m+2)+1=(m-3)*(m+1).

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A001359, A006512, A037074.

EulerPhi[#]DivisorSigma[1,#]&/@Times@@@Select[Partition[Prime[ Range[ 200]],2,1],#[[2]]-#[[1]]==2&] (* Harvey P. Dale, Apr 13 2017 *)

PARI
```
{m=400;p=1;while(p
				
```

a(n)=(m-3)*(m+1), where m=A037074(n).
a(n)=192*A002415(k), where k=A040040(n-1).
a(n) = (A120875(n))^2 - 4 = 4*((A120876(n))^2 - 1). - Lekraj Beedassy, Jul 09 2006

Corrected and extended by Jason Earls, Rick L. Shepherd, Vladeta Jovovic and Klaus Brockhaus, Jun 20 2004

cp's OEIS Frontend

A086870 Primes equal to a product of twin primes minus 1 divided by 2.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A102770 (p*q - 1)/2 where p and q are consecutive odd primes.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A120875 Product of twin primes minus 1.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A094949 Phi(m)*sigma(m), where m is the product of exactly two primes that differ by 2, where phi=A000010, sigma=A000203.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions