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A219528 Primes neighboring a 3-smooth number. 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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.

LINKS

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

EXAMPLE

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

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]

PROG

(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

CROSSREFS

Cf. A003586

Sequence in context: A303436 A334797 A229060 * A341660 A033875 A105581

Adjacent sequences:  A219525 A219526 A219527 * A219529 A219530 A219531

KEYWORD

nonn

AUTHOR

Lei Zhou, Nov 21 2012

STATUS

approved

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Last modified May 20 16:05 EDT 2022. Contains 353874 sequences. (Running on oeis4.)