A337398 Steinhaus' Mega, mod n.

0, 0, 1, 0, 1, 4, 4, 0, 4, 6, 3, 4, 9, 4, 1, 0, 1, 4, 6, 16, 4, 14, 3, 16, 6, 22, 22, 4, 16, 16, 8, 0, 25, 18, 11, 4, 7, 6, 22, 16, 10, 4, 16, 36, 31, 26, 25, 16, 39, 6, 1, 48, 24, 22, 36, 32, 25, 16, 20, 16, 12, 8, 4, 0, 61, 58, 33, 52, 13, 46, 12, 40, 32, 44

Offset

1,6

Comments

This sequence is eventually constant: for all n > Mega, a(n) = Mega.

Links

Table of n, a(n) for n=1..74.

Katie Steckles, Katie's #MegaFavNumbers - the MEGISTON, and Steinhaus-Moser notation, video (2020)

Hugo Steinhaus, Mathematical Snapshots, 2nd ed., New York: Oxford University Press, 1951, p. 19. [These numbers are not mentioned in the first (1938) edition.]

Eric Weisstein's World of Mathematics, Mega.

Wikipedia, Steinhaus-Moser notation.

Index entries for linear recurrences with constant coefficients, signature (1).

Formula

a(n) = (2 in a circle) mod n = (256 in a square) mod n = (...((256 in a triangle) in a triangle)... in a triangle) mod n [with 256 triangles], where k in a triangle = k^k, k in a square = k in k triangles, and k in a circle = k in k squares.

Prog

(PARI) a(n)=my(m=lcm(eulerphi(n), n), t=Mod(256, m), e, last=t); for(i=1, 256, e=lift(t); t=t^(e+m); if(t==last, return(e%n)); last=t); lift(t)%n

Crossrefs

Sequence in context: A138518 A290799 A155836 * A245971 A279365 A164613

Adjacent sequences: A337395 A337396 A337397 * A337399 A337400 A337401

Keyword

nonn

Author

Charles R Greathouse IV, Aug 26 2020

Status

approved