A087732 Smaller of twin primes of the form P=j*P(i)#-1 and P=j*P(i)#+1 with 0 < j < P(i+1), where P(i) denotes i-th prime and P(i)# the i-th primorial number A002110(i).
3, 5, 11, 17, 29, 59, 149, 179, 419, 1049, 2309, 9239, 11549, 25409, 180179, 270269, 300299, 330329, 390389, 420419, 4084079, 8678669, 106696589, 892371479, 2454021569, 3569485919, 4238764529, 4461857399, 4908043139, 6023507489
Offset: 1
Keywords
Examples
17=3*P(2)#-1 and 19=3*P(2)#+1 are twin primes, so 17 is in the sequence, corresponding to i=2, j=3. Again, 182*2633#-1 and 182*2633#+1 are prime twins, with j=182, i=382. These are 1111-digit twin primes. The above prime is a(124). - _Robert G. Wilson v_, Jul 22 2015
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 1..104 (first 128 terms from Robert G. Wilson v) (shortened by _N. J. A. Sloane_, Jan 13 2019)
Programs
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Mathematica
f[n_] := Range[Prime[n + 1] - 1] Times @@ Prime@ Range@ n; s = Select[ Union@ Flatten@ Join[ Array[f, 10] - 1, Array[f, 11, 0] + 1], PrimeQ@# &]; s[[Select[ Range[-1 + Length@ s], s[[#]] + 2 == s[[# + 1]] &]]] (* Robert G. Wilson v, Jul 22 2015 *)
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PARI
do(lastprime)=my(v=List(),P=1,p=2); forprime(q=3,nextprime(lastprime\1+1), P*=p; for(j=1,q-1, if(isprime(j*P-1)&&isprime(j*P+1), listput(v, j*P-1))); p=q); Vec(v) \\ Charles R Greathouse IV, Jul 22 2015
Extensions
Edited by Jud McCranie, Oct 06 2003
Corrected by T. D. Noe, Nov 15 2006
Comments