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A131489
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Anti-primorials, partial products of anti-primes A092680.
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0
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OFFSET
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1,1
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COMMENTS
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Max Alekseyev points out that every term of A066466, except 4, must be of the form 3*2^k such that 3*2^(k+1)-1, 3*2^(k+1)+1 are twin primes. There no such new k+1 (i.e., except known 1,2,6,18) below 1000. In other words, 3*2^n - 1, 3*2^n + 1 are twin primes for n=1,2,6,18. According to these tables: http://www.prothsearch.com/riesel1.html http://www.prothsearch.com/riesel2.html there are no other such n up to 18*10^6. Therefore the next term of A066466 (if it exists) is greater than 3*2^(18*10^6) ~= 10^5418540. Hence the next element of the anti-primorials (if it exists) is greater than 679477248 * 10^5418540 > 10^5418548. [Updated by Max Alekseyev, May 23 2023]
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LINKS
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FORMULA
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a(n) = PRODUCT[k = 1..n] A092680(k).
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EXAMPLE
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a(1) = 3.
a(2) = 3 * 6 = 18.
a(3) = 3 * 6 * 96 = 1728.
a(4) = 3 * 6 * 96 * 393216 = 679477248.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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