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 A221158 Fibonacci numbers with two 1's in the binary representation. 3
 3, 5, 34, 144 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Fibonacci numbers of the form 2^a + 2^b, a>b. Elkies (2014) proved that there are no other terms. This sequence is one row of A222296. - T. D. Noe, Mar 08 2013 LINKS Table of n, a(n) for n=1..4. Noam D. Elkies, Fibonacci numbers with Hamming weight 2, Mathoverflow, 2014. EXAMPLE 144 = 128 + 16 = 2^7 + 2^4, thus it is in the sequence. MATHEMATICA Select[Fibonacci[Range[1000]], DigitCount[#, 2, 1] == 2 &] (* Alonso del Arte, Feb 21 2013 *) PROG (Python) prev = 0 curr = 1 for n in range(3000000): c = 0 # count 1's p = 1 while p<=prev: c += ((prev & p) > 0) if c>2: break p += p if n&1023==0: print '.', if c==2: print prev, prev, curr = curr, prev+curr CROSSREFS Cf. A000045, A004685, A222296. Sequence in context: A354849 A222630 A187993 * A068111 A162444 A305858 Adjacent sequences: A221155 A221156 A221157 * A221159 A221160 A221161 KEYWORD nonn,full,fini AUTHOR Alex Ratushnyak, Feb 20 2013 EXTENSIONS full, fini keywords added by Max Alekseyev, May 13 2014 STATUS approved

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Last modified August 2 21:08 EDT 2024. Contains 374875 sequences. (Running on oeis4.)