A320673 Positive integers m with binary expansion (b_1, ..., b_k) (where k = A070939(m)) such that b_i = [m == 0 (mod i)] for i = 1..k (where [] is an Iverson bracket).
1, 50, 52, 104, 114, 3460, 12298, 29442, 31368, 856592, 1713184, 54822416, 109578256, 109644832, 219156512, 219289664, 438313024, 438579328, 876626048, 877158656, 1034367516, 1753252096, 1754317312, 112208117792, 113290248736, 224416235584, 226580497472
Offset: 1
Examples
The first terms, alongside their binary representation and the divisors encoded therein, are: n a(n) bin(a(n)) First divisors - ----- --------------- -------------------- 1 1 1 1 2 50 110010 1, 2, 5 3 52 110100 1, 2, 4 4 104 1101000 1, 2, 4 5 114 1110010 1, 2, 3, 6 6 3460 110110000100 1, 2, 4, 5, 10 7 12298 11000000001010 1, 2, 11, 13 8 29442 111001100000010 1, 2, 3, 6, 7, 14 9 31368 111101010001000 1, 2, 3, 4, 6, 8, 12
Programs
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PARI
is(n) = my (b=binary(n)); b==vector(#b, k, n%k==0)
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Python
from itertools import count, islice def A320673_gen(startvalue=0): # generator of terms >= startvalue return filter(lambda n:not any(int(b)==bool(n%i) for i,b in enumerate(bin(n)[2:],1)),count(max(startvalue,0))) A320673_list = list(islice(A320673_gen(),10)) # Chai Wah Wu, Dec 12 2022
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