A219433 a(n) is the smallest 3-smooth number such that prime(n)*a(n) + 1 is prime.

1, 2, 2, 4, 2, 4, 6, 12, 2, 2, 12, 4, 2, 4, 6, 2, 12, 6, 4, 8, 4, 4, 2, 2, 4, 6, 6, 6, 24, 2, 4, 2, 6, 4, 8, 6, 24, 4, 48, 2, 2, 6, 2, 4, 18, 4, 72, 12, 24, 12, 2, 2, 6, 2, 6, 6, 8, 6, 4, 2, 6, 2, 4, 6, 6, 48, 6, 16, 6, 24, 96, 2, 6, 4, 12, 12, 24, 6, 8, 4, 2, 16

Offset

1,2

Comments

Conjecture: a(n) < prime(n) except for a(522720).

a(522720)=12582912 > p(522720)=7728803.

Conjecture tested up to a(1000000).

Links

Lei Zhou, Table of n, a(n) for n = 1..10000

Example

prime(1) = 2, 2 * 1 + 1 = 3 is prime, so a(1)=1;
prime(2) = 3, 3 * 2 + 1 = 7 is prime, so a(2)=2;
......
prime(7) = 17, 17 * 1 + 1 = 18 is not prime,
           17 * 2 + 1 = 35 is not prime,
           17 * 3 + 1 = 52 is not prime,
           17 * 4 + 1 = 69 is not prime,
           17 * 6 + 1 = 103 is prime, so a(7)=6

Mathematica

f[n_] := Block[{p2, p3 = 3^Range[0, Floor@ Log[3, n] + 1]}, p2 = 2^Floor[Log[2, n/p3] + 1]; Min[ Select[ p2*p3, IntegerQ]]]; Table[pr=Prime[i]; j=1; fj=0; While[j++; fj=f[fj+1/2]; cp=1+pr*fj; !PrimeQ[cp]]; fj, {i, 115}]

Crossrefs

Cf. A003586.

Sequence in context: A233761 A035096 A066675 * A274879 A222043 A222153

Adjacent sequences: A219430 A219431 A219432 * A219434 A219435 A219436

Keyword

nonn,easy

Author

Lei Zhou, Nov 19 2012

Status

approved