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A062505 Numbers k such that if p is a prime that divides k, then either p + 2 or p - 2 is also prime. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Multiplicative closure of twin primes (A001097).

REFERENCES

Stephan Ramon Garcia and Steven J. Miller, 100 Years of Math Milestones: The Pi Mu Epsilon Centennial Collection, American Mathematical Society, 2019, pp. 35-37.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

EXAMPLE

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.

MATHEMATICA

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] ] (* Jean-Fran├žois Alcover, Feb 23 2012 *)

PROG

(MAGMA) [k:k in [1..170] | forall{p:p in PrimeDivisors(k)| IsPrime(p+2) or IsPrime(p-2)}]; // Marius A. Burtea, Dec 30 2019

CROSSREFS

Range of A072963.

Cf. A001097, A074480.

Sequence in context: A246411 A158333 A293167 * A230104 A093031 A305468

Adjacent sequences:  A062502 A062503 A062504 * A062506 A062507 A062508

KEYWORD

nonn

AUTHOR

Leroy Quet, Jul 09 2001

STATUS

approved

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Last modified September 21 20:10 EDT 2021. Contains 347598 sequences. (Running on oeis4.)