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 A175428 a(n) is the smallest positive integer such that a(n)+a(n-1) is a cube and a(n) is not in {a(1), ..., a(n-1)}. 5
 1, 7, 20, 44, 81, 135, 208, 8, 19, 45, 80, 136, 207, 9, 18, 46, 79, 137, 206, 10, 17, 47, 78, 138, 205, 11, 16, 48, 77, 139, 204, 12, 15, 49, 76, 140, 203, 13, 14, 50, 75, 141, 202, 310, 33, 31, 94, 122, 3, 5, 22, 42, 83, 133, 210, 6, 2, 25, 39, 86, 130, 213, 299, 430, 82 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS It appears that this is a permutation of the positive integers. 4 occurs as a(149). See A034175 for the case where a(n)+a(n-1) is a square. The parity of a(n) equals A133872(n) until n=56 after which there are occasional deviations from the pattern. This is clearly shown by considering the run lengths of the parity for this sequence: 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,2,2,2,2,2,2,2,1,2,3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,2,2,1,2,2,2,1,2,2,3,2,1,2,2,2,3,2,2,2,2,2,2,1,2,2,2,1,2,3,2,2,2,3,2,2,1,2,2,1,... - Jeremy Gardiner, Feb 16 2014 LINKS Jeremy Gardiner, Table of n, a(n) for n = 1..1319 MATHEMATICA a = {1}; For[i = 2, i < 66, i++, k = 1; While[! IntegerQ@ Power[k + a[[i - 1]] && ! MemberQ[a, k], 1/3], k++]; AppendTo[a, k]]; a (* Michael De Vlieger, Jun 02 2015 *) PROG (PARI) v=[1]; n=1; while(n<10^3, if(ispower((v[#v]+n), 3)&&!vecsearch(vecsort(v), n), v=concat(v, n); n=0); n++); v \\ Derek Orr, Jun 01 2015 CROSSREFS Cf. A034175, A011934, A000578 (the cubes), A133872. Sequence in context: A162024 A143058 A298488 * A232599 A011934 A159222 Adjacent sequences:  A175425 A175426 A175427 * A175429 A175430 A175431 KEYWORD nonn,easy AUTHOR John W. Layman, May 10 2010 STATUS approved

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Last modified June 17 04:55 EDT 2021. Contains 345080 sequences. (Running on oeis4.)