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A062505
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If p = prime divides n, then either p+2 or p-2 is prime.
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3
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1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 25, 27, 29, 31, 33, 35, 39, 41, 43, 45, 49, 51, 55, 57, 59, 61, 63, 65, 71, 73, 75, 77, 81, 85, 87, 91, 93, 95, 99, 101, 103, 105, 107, 109, 117, 119, 121, 123, 125, 129, 133, 135, 137, 139, 143, 145, 147, 149, 151, 153, 155, 165
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OFFSET
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1,2
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COMMENTS
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Multiplicative closure of twin primes (A001097).
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LINKS
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Table of n, a(n) for n=1..63.
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EXAMPLE
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35 is included because 35 = 5*7 and both (5+2) and (7-2) are primes.
65=5*13 where the factors are members of twin prime pairs: (3,5) and (11,13), therefore a(29)=65 is a term; but 69 is not because 69=3*23 and 23=A007510(2) is a single prime.
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MATHEMATICA
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nmax = 15 (* corresponding to last twin prime pair (197, 199) *); tp[1] = 3; tp[n_] := tp[n] = (p = NextPrime[tp[n-1]]; While[ !PrimeQ[p+2], p = NextPrime[p]]; p); twins = Flatten[ Table[ {tp[n], tp[n]+2}, {n, 1, nmax}]]; max = Last[twins]; mult[twins_] := Select[ Union[ twins, Apply[ Times, Tuples[twins, {2}], {1}]], # <= max & ]; A062505 = Join[{1}, FixedPoint[mult, twins] ] (* From Jean-François Alcover, Feb 23 2012 *)
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CROSSREFS
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Range of A072963. Cf. A074480.
Sequence in context: A082720 A033037 A158333 * A093031 A143452 A193414
Adjacent sequences: A062502 A062503 A062504 * A062506 A062507 A062508
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet Jul 09 2001
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STATUS
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approved
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