id:A136416 - OEIS Search Results

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Numbers n such that 1+(x+1)^k+(x+1)^n is a primitive polynomial mod 2 for some k where 0<k<n.

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2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 15, 17, 18, 20, 21, 22, 23, 25, 28, 29, 31, 33, 35, 36, 39, 41, 42, 47, 49, 52, 54, 55, 57, 58, 60, 62, 63, 65, 66, 68, 71, 73, 74, 76, 79, 81, 84, 86, 87, 89, 92, 93, 94, 95, 97, 98, 100, 102, 103, 105, 106, 108, 110, 111, 113, 118, 119, 121 (list; graph; listen)

	OFFSET	`1,1`
	COMMENT	`Iff the trinomial T(x)=1+x^k+x^n is irreducible (A073571) then the polynomial T(x+1)=1+(x+1)^k+(1+x)^n is irreducible.` `The order of T(x+1) is in general different form the order of T(x).` `So this seqnecne is different form A073726: for example, 1+(x+1)^7+(1+x)^10 is primitive but 1+(x+1)^3+(1+x)^10 is not (while 1+x^7+x^10 and 1+x^3+x^10 are mutual reciprocal and have the same order).`
	LINKS	`Joerg Arndt (arndt(AT)jjj.de), Mar 31 2008, Table of n, a(n) for n = 1..211` `Joerg Arndt, fxtbook (draft of the book "Algorithms for Programmers")`
	EXAMPLE	`10 is in the sequence because 1+(x+1)^7+(1+x)^10 is primitive mod 2`
	CROSSREFS	`Adjacent sequences: A136413 A136414 A136415 this_sequence A136417 A136418 A136419` `Sequence in context: A014133 A070115 A073571 this_sequence A072497 A039217 A131511`
	KEYWORD	`nonn`
	AUTHOR	`Joerg Arndt (arndt(AT)jjj.de), Mar 31 2008`

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Last modified January 7 17:35 EST 2009. Contains 152824 sequences.

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