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Search: id:A050229
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| A050229 |
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Numbers n such that for any x, 1<=x<=n-1, there is y, 0<=y<=n-2, such that x^2 ( mod n) = 2^y ( mod n). |
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+0
2
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| 1, 2, 3, 5, 11, 13, 19, 29, 37, 53, 59, 61, 67, 83, 101, 107, 131, 139, 149, 163, 173, 179, 181, 197, 211, 227, 269, 293, 317, 347, 349, 373, 379, 389, 419, 421, 443, 461, 467, 491, 509, 523, 541, 547, 557, 563, 587, 613, 619, 653, 659, 661, 677, 701, 709, 757, 773, 787, 797, 821, 827, 829, 853, 859, 877, 883, 907, 941, 947
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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It seems that sequence consists of {1,2} union A001122. The sequence differs from A082595 because here the multiplicity is not important (see example : P contains two 5's and Q is required to have at least one 5, not necessarily 2 5's.)
Numbers n for which there is a permutation of 0..n-1 such that each number is the sum of all the previous, plus 1, mod n. - Ron Hardin (rhhardin(AT)att.net), Dec 28 2007
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EXAMPLE
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The set of values for x^2 mod 19, 1<=x<=18, is P=[1, 4, 9, 16, 6, 17, 11, 7, 5, 5, 7, 11, 17, 6, 16, 9, 4, 1], the set of values for 2^y mod 19, 0<=y<=n-2 is Q= [1, 2, 4, 8, 16, 13, 7, 14, 9, 18, 17, 15, 11, 3, 6, 12, 5, 10] which contains all values in P, hence 19 is in the sequence.
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PROGRAM
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(PARI) for(n=1, 450, if(sum(y=1, n-1, if(setsearch(Set(vector(n-1, x, 2^(x-1)%n)), y), 0, 1))==0, print1(n, ", ")))
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CROSSREFS
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Cf. A001122, A082595.
Sequence in context: A153002 A042999 A089194 this_sequence A053184 A020607 A128425
Adjacent sequences: A050226 A050227 A050228 this_sequence A050230 A050231 A050232
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), May 08 2003
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EXTENSIONS
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More terms from Ron Hardin (rhhardin(AT)att.net), Dec 28 2007
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