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

1,1

Comments

Probably an infinite sequence. Using the UB874 program (UBASIC) I found the first 123 primes of the sequence for i <= 382. I think I have a proof that the sequence is infinite.

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)

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A000040, A002110, A086916, A087700, A087731, A088676, A060735.

Sequence in context: A147023 A108402 A090795 * A278053 A174916 A309433

Adjacent sequences: A087729 A087730 A087731 * A087733 A087734 A087735

Keyword

nonn

Author

Pierre CAMI, Sep 29 2003

Extensions

Edited by Jud McCranie, Oct 06 2003

Corrected by T. D. Noe, Nov 15 2006

Status

approved