A250037 Numbers n such that m = floor(n/4) is not coprime to n and, if nonzero, m is also a term of the sequence.

2, 3, 8, 10, 12, 15, 32, 34, 40, 42, 48, 50, 51, 60, 63, 128, 130, 136, 138, 160, 162, 168, 170, 171, 192, 194, 195, 200, 202, 204, 207, 240, 242, 243, 252, 255, 512, 514, 520, 522, 544, 546, 552, 554, 555, 640, 642, 648, 650, 651, 672, 674, 675, 680, 682

Offset: 1

Author

Stanislav Sykora, Dec 07 2014

Keywords

• nonn
• base

Comments

See the comments in A250041 which all apply, except for the setting of the base, b=4. In particular, they define the property RTNC(b).

If x =12*k+j, 0 <= j <= 11, then x is in the sequence iff either j is in {0,2,3} and 3*k is in the sequence, or j is in {4,6} and 3*k+1 is in the sequence, or j is in {8,10} and 3*k+2 is in the sequence. - Robert Israel, Dec 22 2014

Links

• Stanislav Sykora, Table of n, a(n) for n = 1..10000
• Stanislav Sykora, PARI/GP scripts for genetic threads, with code and comments.
• Wikipedia, Coprime integers

Crossrefs

Cf. A250036, A250041.

Other lists of right-truncatable numbers with the property RTNC(b):

A005823 (b=3), A250039 (b=16), A250041 (b=10), A250043 (b=9), A250045 (b=8), A250047 (b=7), A250049 (b=6), A250051 (b=5).

Programs

Maple

S:= {}:
for n from 1 to 1000 do
  m:= floor(n/4);
  if igcd(m,n) = 1 then next fi;
  if m > 0 and not member(m,S) then next fi;
  S:= S union {n}
od:
S; # if using Maple 11 or earlier, uncomment the next line
# sort(convert(S,list)); # Robert Israel, Dec 22 2014

PARI

See the link.

PARI

is_rtnc(n, b=4) = {while (((m=gcd(n\b, n)) != 1), if (m == 0, return (1)); n = n\b; ); return (0); } \\ Michel Marcus, Jan 22 2015