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Search: id:A111176
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| A111176 |
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Sophie Germain 4-almost primes. |
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+0
6
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| 40, 220, 580, 712, 808, 812, 904, 940, 1062, 1192, 1444, 1592, 1612, 1690, 1812, 1876, 2002, 2152, 2212, 2236, 2254, 2488, 2502, 2562, 2650, 2662, 2788, 3010, 3052, 3064, 3112, 3162, 3208, 3258, 3272, 3352, 3448, 3550, 3580, 3820, 3832, 3892, 3910, 4012
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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4-almost primes P such that 2*P + 1 are also 4-almost primes. There should also be 4-almost prime chains of length k analogous to Cunningham chains of the first kind and Tomaszewski chains of the first kind. A 4-almost prime chain of length k is a sequence of 4-almost primes a(1) < a(2) < ... < a(k) such that a(i+1) = 2*a(i) + 1 for i = 1, ..., k-1. There are no such chains beginning with integers under 1200.
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FORMULA
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{a(n)} = a(n) is an element of A014613 and 2*a(n)+1 is an element of A014613.
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EXAMPLE
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n p 2*p+1
1 40 = 2^3 * 5 81 = 3^4
2 220 = 2^2 * 5 * 11 441 = 3^2 * 7^2
3 580 = 2^2 * 5 * 29 1161 = 3^3 * 43
4 712 = 2^3 * 89 1425 = 3 * 5^2 * 19
5 808 = 2^3 * 101 1617 = 3 * 7^2 * 11
6 812 = 2^2 * 7 * 29 1625 = 5^3 * 13
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CROSSREFS
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Cf. A005384, A014613, A111153, A111168, A111170, A111171, A111173.
Sequence in context: A089548 A117216 A077818 this_sequence A072108 A074360 A068790
Adjacent sequences: A111173 A111174 A111175 this_sequence A111177 A111178 A111179
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost2(AT)yahoo.com), Oct 22 2005
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EXTENSIONS
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Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Oct 22 2005
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