A290960 Numbers k such that A276976(k) > A270096(k).

8, 32, 56, 64, 96, 128, 144, 155, 170, 176, 192, 196, 204, 215, 221, 224, 238, 248, 255, 256, 272, 288, 320, 322, 336, 341, 352, 368, 372, 374, 384, 432, 448, 465, 476, 496, 510, 512, 527, 544, 574, 576, 608, 612, 623, 635, 640, 644, 645, 658, 663, 672, 682, 697, 704, 714, 731, 736, 744

Offset: 1

Author

Altug Alkan, Aug 15 2017, following a suggestion from N. J. A. Sloane

Keywords

• nonn

Comments

Odd terms are 155, 215, 221, 255, 341, 465, 527, 623, 635, 645, 663, ...

These odd terms are odd numbers k such that (k mod A002322(k)) > (k mod A002326((k-1)/2)). - Amiram Eldar and Thomas Ordowski, Nov 28 2019

Examples

			8 is a term because A276976(8) = 4 while A270096(8) = 3.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002322, A002326, A270096, A276976.

Programs

Maple

A270096:= proc(n) local d, b, t, m, c;
  d:= padic:-ordp(n, 2);
  b:= n/2^d;
  t:= 2 &^ n mod n;
  m:= numtheory:-mlog(t, 2, b, c);
  if m < d then m:= m + c*ceil((d-m)/c) fi;
  m
end proc:
A270096(1):= 0:
A276976:= proc(n) local lambda;
  lambda:= numtheory:-lambda(n);
  if n mod lambda = 0 then lambda
  elif n mod 8 = 0 and (n-2) mod lambda = 0 then lambda+2
  else n mod lambda
  fi
end proc:
A276976(1):= 0:
A276976(8):= 4:
A276976(24):= 4:
select(n -> A276976(n) > A270096(n), [$1..1000]); # Robert Israel, Aug 16 2017

Mathematica

With[{nn = 750}, Select[Range@ nn, Function[n, SelectFirst[Range[nn/4 + 10], Function[m, AllTrue[Range[2, n - 1], PowerMod[#, m , n] == PowerMod[#, n , n] &]]] > SelectFirst[Range[nn/4 + 10], PowerMod[2, n, n] == PowerMod[2, #, n] &]]]] (* Michael De Vlieger, Aug 15 2017 *)