A219528 Primes neighboring a 3-smooth number.

2, 3, 5, 7, 11, 13, 17, 19, 23, 31, 37, 47, 53, 71, 73, 97, 107, 109, 127, 163, 191, 193, 257, 383, 431, 433, 487, 577, 647, 769, 863, 971, 1151, 1153, 1297, 1459, 2591, 2593, 2917, 3457, 3889, 4373, 6143, 6911, 8191, 8747, 10369, 12289, 13121, 15551, 17497, 18433, 23327, 27647, 39367, 52489, 62207, 65537, 73727

Offset: 1

Author

Lei Zhou, Nov 21 2012

Keywords

• nonn

Comments

Prime numbers of the form of 2^j*3^k +/- 1, which may be called "near-3-smooth primes".

Such prime numbers can often be proved prime by OpenPFGW.

Examples

			a(1)=2=1+1, where A003586(1)=1;
a(2)=3=2+1, where A003586(2)=2;
...
a(59)=73727=2^13*3^2-1, where A003586(97)=2^13*3^2=73728.
		

Links

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

Crossrefs

Cf. A003586

Programs

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]]];
a={};ct=0;tsm=1;While[ct<59,cp=tsm-1;If[(PrimeQ[cp])&&(!MemberQ[a,cp]),a=Append[a,cp];ct++];cp=cp+2;If[(PrimeQ[cp])&&(!MemberQ[a,cp]),a=Append[a,cp];ct++];tsm=f[tsm]];Print[a]

PARI

list(lim)=my(v=List([2]), N); for(n=0, log(lim\2)\log(3), N=2*3^n; while(N<=lim, if(ispseudoprime(N-1),listput(v, N-1)); if(ispseudoprime(N+1), listput(v, N+1)); N<<=1)); vecsort(Vec(v),,8) \\ Charles R Greathouse IV, Nov 21 2012