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 A308811 Numbers k such that the binary plot of the list of divisors of k has reflection symmetry. 1
 1, 2, 3, 4, 8, 10, 15, 16, 32, 64, 128, 136, 170, 255, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 32896, 34952, 43690, 65535, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The sequence is infinite as it contains every power of 2 (A000079). The product of the first five Fermat primes (A019434), 4294967295 = 3 * 5 * 17 * 257 * 65537, is also a member of this sequence. Every term belongs to A135772. The first 48 terms are all of the form Sum_{i=1..t} 2^(k*t-1) for some k > 0 and t > 0 (see binary plot in Links section). LINKS Rémy Sigrist, Binary plot of the first 48 terms FORMULA A295368(a(n)) = a(n). EXAMPLE Regarding 170: - the divisors of 170 are: 1, 2, 5, 10, 17, 34, 85, 170, - in binary: "1", "10", "101", "1010", "10001", "100010", "1010101", "10101010", - the corresponding binary plot is:   .             1         .             #     .         1 0           .         #       .     1 0 1             .     #   #         . 1 0 1 0               . #   #         1 0 0 0 1               # .     #       1 0 0 0 1 0             #     . #     1 0 1 0 1 0 1           #   #   # . #   1 0 1 0 1 0 1 0         #   #   #   # .                   .                       .                     .                       . - this binary plot has reflection symmetry, - hence 170 belongs to this sequence. PROG (PARI) is(n) = { my (d=Vecrev(divisors(n))); if (#binary(d)==#d, for (b=0, #d-1, my (t=0); for (i=1, #d, if (bittest(d[i], b), t+=2^(i-1))); if (t!=d[b+1], return (0))); return (1), return (0)) } CROSSREFS Cf. A000079, A019434, A135772, A295368. Sequence in context: A242762 A005542 A037171 * A295296 A186417 A207644 Adjacent sequences:  A308808 A308809 A308810 * A308812 A308813 A308814 KEYWORD nonn,base AUTHOR Rémy Sigrist, Jul 08 2019 STATUS approved

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Last modified February 16 21:46 EST 2020. Contains 331975 sequences. (Running on oeis4.)