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A050229
Numbers k such that for any x in 1..k-1 there exists a y in 0..k-2 such that x^2 == 2^y (mod k).
2
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
OFFSET
1,2
COMMENTS
It seems that the 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 k for which there is a permutation of 0..k-1 such that each number is the sum of all the previous numbers, plus 1, mod k. - R. H. Hardin, Dec 28 2007
Positive numbers k such that x^(k-1) + x^(k-2) + x^(k-3) + ... + x + 1 is irreducible over GF(2). - Arkadiusz Wesolowski, Nov 20 2012
All terms > 1 are prime. Appears to be set of numbers k such that the sequence 2^n mod k has period length of k-1. - Gary Detlefs, May 15 2014
FORMULA
a(n) = A071642(n) + 1. - Arkadiusz Wesolowski, Nov 20 2012
EXAMPLE
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.
PROG
(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, ", ")))
CROSSREFS
Sequence in context: A153002 A042999 A089194 * A224321 A053184 A228445
KEYWORD
nonn
AUTHOR
Benoit Cloitre, May 08 2003
EXTENSIONS
More terms from R. H. Hardin, Dec 28 2007
STATUS
approved