A356353 Numbers k such that A356352(k) <> 1.
0, 3, 7, 12, 15, 31, 48, 51, 56, 60, 63, 127, 192, 195, 204, 207, 240, 243, 252, 255, 448, 455, 504, 511, 768, 771, 780, 783, 816, 819, 828, 831, 960, 963, 972, 975, 992, 1008, 1011, 1020, 1023, 2047, 3072, 3075, 3084, 3087, 3120, 3123, 3132, 3135, 3264, 3267
Offset: 1
Examples
The first terms, alongside their binary expansions and A356352(a(n)), are: n a(n) bin(a(n)) A356352(a(n)) -- ---- ---------- ------------- 1 0 0 0 2 3 11 2 3 7 111 3 4 12 1100 2 5 15 1111 4 6 31 11111 5 7 48 110000 2 8 51 110011 2 9 56 111000 3 10 60 111100 2 11 63 111111 6 12 127 1111111 7 13 192 11000000 2 14 195 11000011 2 15 204 11001100 2 16 207 11001111 2
Links
Programs
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PARI
is(n) = { my (r=[]); while (n, my (v=valuation(n+n%2, 2)); n\=2^v; r=concat(v, r)); gcd(r)!=1 } -
PARI
See Links section.
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Python
from math import gcd from itertools import groupby def ok(n): if n == 0: return True # by convention of A356352 return gcd(*(len(list(g)) for k, g in groupby(bin(n)[2:]))) != 1 print([k for k in range(3268) if ok(k)]) # Michael S. Branicky, Oct 15 2022
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