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 A054204 Integers expressible as sums of distinct even-subscripted Fibonacci numbers. 5
 1, 3, 4, 8, 9, 11, 12, 21, 22, 24, 25, 29, 30, 32, 33, 55, 56, 58, 59, 63, 64, 66, 67, 76, 77, 79, 80, 84, 85, 87, 88, 144, 145, 147, 148, 152, 153, 155, 156, 165, 166, 168, 169, 173, 174, 176, 177, 199, 200, 202, 203, 207, 208, 210, 211, 220, 221, 223, 224, 228, 229 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Number of partitions of a(n) into sums of distinct Fibonacci numbers is (n+1)st term of Stern's Diatomic series A002487. This sequence has A046815 as a subsequence. LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 Marjorie Bicknell-Johnson, The least integer having p Fibonacci representations (p prime), Fibonacci Quarterly 40 (2002), pp. 260-265. Marjorie Bicknell-Johnson, Stern's Diatomic Array Applied to Fibonacci Representations, Fibonacci Quarterly 41 (2003), pp. 169-180. FORMULA Subscripts in Zeckendorf representation of a(n) are 2(e+1) where e is exponent used to write n as sum of powers of 2. EXAMPLE a(9)=22 since 9=2^3+2^0 and 22=F(2(3+1)) + F(2(0+1)) = F(8) + F(2). MATHEMATICA fibEvenCount[n_] := Plus @@ (Reverse @ IntegerDigits[n, 2])[[2 ;; -1 ;; 2]]; evenIndexed = fibEvenCount /@ Select[Range[10000], BitAnd[#, 2 #] == 0 &]; Position[evenIndexed, _?(# == 0 &)] // Flatten (* Amiram Eldar, Jan 20 2020*) PROG (PARI) my(m=Mod('x, 'x^2-3*'x+1)); a(n) = subst(lift(subst(Pol(binary(n)), 'x, m)), 'x, 3); \\ Kevin Ryde, Nov 25 2020 CROSSREFS Cf. A002487, A014417, A046815. Cf. A022290, A062877 (odd-indexed Fibonaccis). Distinct additive closure of A001906. Sequence in context: A193532 A068056 A006520 * A050003 A002156 A285033 Adjacent sequences:  A054201 A054202 A054203 * A054205 A054206 A054207 KEYWORD nonn AUTHOR Marjorie Bicknell-Johnson (marjohnson(AT)earthlink.net), Apr 30 2000 STATUS approved

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Last modified June 30 11:55 EDT 2022. Contains 354939 sequences. (Running on oeis4.)