A047978 - OEIS

A047978

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

17, 71, 881, 2591, 179999, 206081, 388961, 2268449, 2836961, 3612671, 6329681, 6415361, 10342151, 18800711, 28486151, 32080049, 40878881, 89753201, 97050311, 127552391, 154844801, 183169799, 230953031, 344531249

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

EXAMPLE

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

MATHEMATICA

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

PROG

(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

(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

CROSSREFS

Cf. A047976-A047979.

Sequence in context: A320895 A288748 A069496 * A050524 A214530 A087514

Adjacent sequences: A047975 A047976 A047977 * A047979 A047980 A047981

KEYWORD

nonn

AUTHOR

Naohiro Nomoto

STATUS

approved