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Search: id:A067526
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| A067526 |
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Numbers n such that n - 2^k is a prime or 1 for all k satisfying 0 < k, 2^k < n. |
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+0
6
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OFFSET
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1,1
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COMMENT
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Is the sequence finite?
Let n be the next (so far unknown) term. If n>2^(p-1) then p divides n for every odd prime p. This yields, with some extra testing, that n is divisible by the first 1230 odd primes, so n>10^4300. It should be possible to show that there exists an m such that for all n>m the product of the odd primes <=n is greater than 2^(nextprime(n)-1). This would implie that the above sequence is finite. - Sascha Kurz (sascha.kurz(AT)uni-bayreuth.de), Mar 18 2002
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EXAMPLE
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45 belongs to this sequence as 45- 2, 45-4, 45-8, 45-16, 45-32 etc. i.e. 43, 41,37,29 and 13 are all primes.
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MATHEMATICA
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f[n_] := Block[{k = 1}, While[2^k < n, k++ ]; k--; k]; Do[ a = Table[n - 2^k, {k, 1, f[n]} ]; If[ a[[ -1]] == 1, a = Drop[a, -1]]; If[ Union[ PrimeQ[a]] == {True}, Print[n]], {n, 5, 10^7, 2} ]
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CROSSREFS
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Cf. A039669 (n-2^k is prime).
Sequence in context: A082922 A036971 A000702 this_sequence A101760 A165713 A105148
Adjacent sequences: A067523 A067524 A067525 this_sequence A067527 A067528 A067529
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KEYWORD
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easy,nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Feb 17 2002
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EXTENSIONS
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Edited by Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 18 2002
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