A325204 -id:A325204 - cp's OEIS frontend

A325255 3-smooth numbers k such that k+1 and (k+2)/2 are prime.

2, 4, 12, 36, 72, 192, 1152, 2592, 2916, 1492992, 1990656, 5308416, 28311552, 6879707136, 1761205026816, 5566277615616, 79164837199872, 3799912185593856, 115422332637413376, 1332669751402954752, 4803028329503971872

Offset: 1

Robert Israel, Sep 05 2019

nonn

Numbers k of the form 2^a*3^b such that k+1 and (k+2)/2 are prime.
All terms except 2 and 4 are in A325204.
All terms except 4 end in 2 or 6.

			a(3)=12 is a term because 12=2^2*3 and 13 and 14/2 are prime.

Ray Chandler, Table of n, a(n) for n = 1..41 (terms < 10^1000; first 39 terms from Robert Israel)

Cf. A003586, A325204, A327240.

N:= 10^100: # to get terms <= N
sort(select(t -> isprime(t+1) and isprime((t+2)/2), [seq(seq(2^i*3^j, i = 1 .. ilog2(N/3^j)), j=0..floor(log[3](N)))]));

A327240 3-smooth numbers k such that k-1 and (k-2)/2 are prime.

Original entry on oeis.org

6, 8, 12, 24, 48, 108, 384, 864, 8748, 995328, 2348273369088, 7421703487488, 21422803359744, 3470494144278528, 161919374795459002368, 1838129271989302091317248, 2168345519443636233418208968704, 28070062609828769223367060340342784

Offset: 1

Ray Chandler, Sep 14 2019

nonn

Numbers k of the form 2^a*3^b such that k-1 and (k-2)/2 are prime.
For all terms k except 6 and 8, k-2 is in A325204.
All terms except 6 and 12 end in 4 or 8.

			a(3)=12 is a term because 12=2^2*3 and 11 and 10/2 are prime.

Ray Chandler, Table of n, a(n) for n = 1..39 (terms < 10^1000)

Cf. A003586, A325204, A325255.

nmax = 10^35;
Select[Sort[Flatten[Table[2^i*3^j, {j, 0, Log[3, nmax]}, {i, Log[2, nmax/3^j]}]]], PrimeQ[# - 1] && PrimeQ[(# - 2)/2] &]

cp's OEIS Frontend

A325255 3-smooth numbers k such that k+1 and (k+2)/2 are prime.

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