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 1-3 of 3 results.

A128551 a(n) = p, the lesser of twin primes (p, q=p+2) such that p*q - p - q is prime.

Original entry on oeis.org

3, 5, 29, 71, 107, 191, 239, 569, 881, 1091, 1289, 1619, 1721, 1931, 1997, 2081, 2087, 2129, 2309, 2381, 2549, 2591, 2729, 3299, 3359, 3527, 3851, 4229, 4241, 4271, 4649, 5279, 5501, 5651, 6299, 7127, 7349, 7547, 7589, 7757, 8219, 8969, 9437, 10037
Offset: 1

Views

Author

Zak Seidov, Mar 10 2007

Keywords

Comments

Or, p prime such that p+2 and p^2-2 are primes.

Examples

			3, 5 and 3*5-3-5=7 are prime; 5, 7 and 5*7-5-7=23 are prime; 29, 31 and 29*31-29-31=839 are primes.

Links

Crossrefs

Cf. A096342, A126148, A128547, A128548, A128550.

Programs

  • Mathematica
    Clear[lst,f1,f2,n,p]; f1[n_]:=PrimeQ[n+2]; f2[n_]:=PrimeQ[n*(n+2)-((n+2)+n)]; lst={};Do[p=Prime[n];If[f1[p]&&f2[p],AppendTo[lst,p]],{n,7!}];lst (* Vladimir Joseph Stephan Orlovsky, Sep 19 2009 *)
tpQ[{a_,b_}]:=b-a==2&&PrimeQ[a*b-a-b]; Transpose[Select[Partition[ Prime[ Range[ 1300]],2,1],tpQ]][[1]] (* Harvey P. Dale, May 22 2014 *)

A126334 Lesser of twin primes (p,q=p+2) such that p*q-p-q and p*q+p+q are primes.

Original entry on oeis.org

3, 5, 17681, 21377, 21587, 33599, 41201, 41411, 70139, 74759, 84629, 109619, 114197, 130619, 155861, 160481, 174467, 219407, 222977, 223439, 230999, 235787, 243431, 284129, 285641, 287279, 300929, 325079, 373211, 386987, 389297, 397151
Offset: 1

Views

Author

Zak Seidov, Mar 10 2007

Keywords

Comments

Or, primes p such that p+2, p^2-2 and 2 + 4*p + p^2 are primes. Intersection of A128550 and A128551.
The number of such p's <= 10^n: 2, 2, 2, 2, 11, 56, 320, 1772, ..., . - Robert G. Wilson v, Mar 11 2007

Links

Crossrefs

Cf. A096342, A126148, A128547, A128548, A128550, A128551.

Programs

  • Mathematica
    fQ[n_] := Block[{p = Prime[n], q = Prime[n + 1]}, p + 2 == q && PrimeQ[p*q - p - q] && PrimeQ[p*q + p + q]]; lst = {}; Do[ If[ fQ@n == True, AppendTo[lst, Prime@n]; Print@ Prime@n], {n, 39055}] (* Robert G. Wilson v, Mar 11 2007 *)

Extensions

More terms from Robert G. Wilson v, Mar 11 2007

A168536 The lesser of twin primes p such that p*q+a+b+c are also the lesser of twin primes, (p and q are twin primes, p+2=q, a=p-1,b=(p+q)/2,c=q+1).

Original entry on oeis.org

11, 101, 179, 347, 569, 1049, 1229, 1301, 1487, 1667, 3557, 4127, 6089, 6761, 8627, 9041, 10067, 11939, 12251, 14321, 19421, 25847, 28571, 29207, 30011, 30869, 31541, 33329, 33587, 36791, 38459, 39509, 39839, 40427, 43049, 49529, 50591, 50969
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Nov 28 2009

Keywords

Links

Crossrefs

Cf. A001359, A126334, A128550, A128551

Programs

  • Mathematica
    lst={};Do[p=Prime[n];q=p+2;If[PrimeQ[q],a=p-1;b=p+1;c=q+1;If[PrimeQ[p*q+a+b+c]&&PrimeQ[p*q+a+b+c+2],AppendTo[lst,p]]],{n,8!}];lst
Select[Partition[Prime[Range[5300]],2,1],#[[2]]-#[[1]]==2&&AllTrue[#[[1]]^2+5#[[1]]+{3,5},PrimeQ]&][[;;,1]] (* Harvey P. Dale, Sep 23 2023 *)
Showing 1-3 of 3 results.

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

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