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A294919 Numbers n such that 2^(n-1), (2*n-1)*(2^((n-1)/2)), (4*ceiling((1/4)*n)-2), and (2^((n+1)/2) + floor((3/4)*n)*2^(((n+1)/2)+1)) are all congruent to 1 (mod n). 1
5, 13, 29, 37, 53, 61, 101, 109, 149, 157, 173, 181, 197, 229, 269, 277, 293, 317, 349, 373, 389, 397, 421, 461, 509, 541, 557, 613, 653, 661, 677, 701, 709, 733, 757, 773, 797, 821, 829, 853, 877, 941, 997, 1013, 1021, 1061, 1069, 1093, 1109, 1117, 1181, 1213 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

It appears that A007521 is a subsequence.

a(118) = 3277 = 29*113 is the first nonprime term.

LINKS

Table of n, a(n) for n=1..52.

Jonas Kaiser, On the relationship between the Collatz conjecture and Mersenne prime numbers, arXiv:1608.00862 [math.GM], 2016.

MATHEMATICA

okQ[n_] := AllTrue[{2^(n-1), (2*n-1)*(2^((n-1)/2)), (4*Ceiling@(n/4) - 2), (2^((n+1)/2) + Floor@((3/4)*n)*2^(((n+1)/2) + 1))}, Mod[#, n] == 1&];

Select[Range[1300], okQ] (* Jean-Fran├žois Alcover, Feb 18 2019 *)

PROG

(PARI) isok(n) = (n%2) && lift((Mod(2, n)^(n-1))==1)&&lift((Mod((2*n-1), n)*Mod(2, n)^((n-1)/2)) == 1)&&lift((Mod(((4*ceil((1/4)*n)-2)), n) )== 1)&&lift((Mod(2, n)^((n+1)/2) +Mod(floor((3/4)*n), n)*Mod(2, n)^(((n+1)/2)+1 ))== 1)

CROSSREFS

Cf. A007521, A070179, A244626, A293394, A294717.

Sequence in context: A100877 A261580 A007521 * A213050 A216822 A217466

Adjacent sequences:  A294916 A294917 A294918 * A294920 A294921 A294922

KEYWORD

nonn

AUTHOR

Jonas Kaiser, Nov 10 2017

EXTENSIONS

More terms from Alois P. Heinz, Nov 10 2017

STATUS

approved

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Last modified July 9 22:46 EDT 2020. Contains 335570 sequences. (Running on oeis4.)