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A102476 Least modulus with 2^n square roots of 1. 5
1, 3, 8, 24, 120, 840, 9240, 120120, 2042040, 38798760, 892371480, 25878772920, 802241960520, 29682952539240, 1217001054108840, 52331045326680120, 2459559130353965640, 130356633908760178920, 7691041400616850556280 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The number of square roots of 1 in any modulus is a power of 2.

Another way of expressing the same:  These are also the record setting values of m for the number of solutions to "m*k+1 is a square", for some k, 0<=k<=m. There is 1 solution for a(0)=m=1, and for m = a(n), n>0, there is the first occurrence of 2^n solutions. Compare with A006278.  - Richard R. Forberg, Mar 18 2016

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..351

FORMULA

a(n) = 4(p(n-1))# = 4*A002110(n-1) for n >= 2. Least k with A060594(k) = 2^n.

EXAMPLE

a(3) = 24 because 24 is the least modulus with 2^3 square roots of 1, namely 1,5,7,11,13,17,19,23.

MATHEMATICA

{1, 3}~Join~Table[4 Product[Prime[k], {k, n}], {n, 17}] (* Michael De Vlieger, Mar 27 2016 *)

nxt[{a_, p_}] := {a*NextPrime[p], NextPrime[p]}; Join[{1, 3}, NestList[nxt, {8, 2}, 20][[All, 1]]] (* or *) Join[{1, 3}, 4*FoldList[ Times, Prime[ Range[ 21]]]](* Harvey P. Dale, Dec 18 2016 *)

CROSSREFS

Cf. A060594, A002110, A006278.

Sequence in context: A174662 A002104 A102919 * A302109 A220486 A180380

Adjacent sequences:  A102473 A102474 A102475 * A102477 A102478 A102479

KEYWORD

easy,nonn

AUTHOR

David W. Wilson, Jan 10 2005

STATUS

approved

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Last modified February 16 18:53 EST 2019. Contains 320165 sequences. (Running on oeis4.)