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 A309079 For any n > 0: consider the strictly increasing finite sequences of integers whose concatenation of terms, in binary and without leading zeros, equals that of n; a(n) is the minimal sum of the terms of such a finite sequence. 1
 1, 2, 3, 4, 5, 3, 4, 8, 9, 10, 5, 5, 6, 7, 8, 16, 17, 18, 19, 6, 7, 8, 9, 9, 10, 11, 6, 7, 8, 9, 10, 32, 33, 34, 35, 36, 9, 10, 11, 10, 11, 12, 13, 14, 15, 11, 12, 17, 18, 19, 20, 7, 8, 9, 10, 11, 12, 13, 14, 8, 9, 10, 11, 64, 65, 66, 67, 68, 69, 70, 71, 12 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Any integer appear in the sequence: - for any m > 0 with binary expansion Sum_{k >= 0} b_k * 2^k, - let n = (Sum_{k >= 0} b_k * 2^Sum_{j >= k} ((1+j) * b_j))/2, - then a(n) = m, - for example (in binary): a("1101000") = "1" + "10" + "1000" = "1011". LINKS Rémy Sigrist, Table of n, a(n) for n = 1..8192 Rémy Sigrist, PARI program for A309079 FORMULA a(n) <= n with equality iff n is a power of two or the binary concatenation of 2^k and m for some k >= 0 and m <= 2^k. a(2*n) <= 2*a(n). a(2*n + 1) <= 2*a(n) + 1. a(A164894(k)) = A000225(k) for any k > 0. EXAMPLE The first terms, alongside the corresponding finite sequences, are: n a(n) bin(n) bin(seq) -- ---- ------ -------- 1 1 1 (1) 2 2 10 (10) 3 3 11 (11) 4 4 100 (100) 5 5 101 (101) 6 3 110 (1,10) 7 4 111 (1,11) 8 8 1000 (1000) 9 9 1001 (1001) 10 10 1010 (1010) 11 5 1011 (10,11) 12 5 1100 (1,100) 13 6 1101 (1,101) 14 7 1110 (1,110) 15 8 1111 (1,111) 16 16 10000 (10000) 17 17 10001 (10001) 18 18 10010 (10010) 19 19 10011 (10011) 20 6 10100 (10,100) 21 7 10101 (10,101) PROG (PARI) See Links section. CROSSREFS Cf. A000225, A143789, A164894. Sequence in context: A117607 A215092 A345018 * A194551 A212644 A351285 Adjacent sequences: A309076 A309077 A309078 * A309080 A309081 A309082 KEYWORD nonn,base AUTHOR Rémy Sigrist, Jul 11 2019 STATUS approved

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Last modified November 28 19:28 EST 2023. Contains 367419 sequences. (Running on oeis4.)