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 A047978 Let (p1,p2), (p3,p4) be pairs of twin primes with p1*p2=p3+p4-1; sequence gives values of p3. 3

%I #9 May 19 2023 12:57:12

%S 17,71,881,2591,179999,206081,388961,2268449,2836961,3612671,6329681,

%T 6415361,10342151,18800711,28486151,32080049,40878881,89753201,

%U 97050311,127552391,154844801,183169799,230953031,344531249

%N Let (p1,p2), (p3,p4) be pairs of twin primes with p1*p2=p3+p4-1; sequence gives values of p3.

%H Charles R Greathouse IV, <a href="/A047978/b047978.txt">Table of n, a(n) for n = 1..10000</a>

%e E.g. 5*7=17+19-1,11*13=71+73-1.

%t Select[(Times@@#-1)/2&/@Select[Partition[Prime[Range[3000]],2,1],#[[2]]-#[[1]]==2&],AllTrue[ #+{0,2},PrimeQ]&] (* _Harvey P. Dale_, May 19 2023 *)

%o (PARI) list(lim)=my(v=List(),p=3,r); forprime(q=5,sqrtint(lim\1*2+2)+1, if(q-p==2 && isprime(r=p*q\2) && isprime(r+2), listput(v,r)); p=q); Vec(v) \\ _Charles R Greathouse IV_, Sep 29 2015

%o (PARI) is(n)=my(p=sqrtint(2*n+1)); p*(p+2)==2*n+1 && isprime(n) && isprime(n+2) && isprime(p) && isprime(p+2) \\ _Charles R Greathouse IV_, Sep 29 2015

%Y Cf. A047976-A047979.

%K nonn

%O 1,1

%A _Naohiro Nomoto_

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Last modified July 14 00:54 EDT 2024. Contains 374290 sequences. (Running on oeis4.)