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 A268133 If a(n) is not a square, then a(n+1) = a(n) + a(n-1), else a(n+1) is the smallest positive integer not occurring earlier. 1
 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 4, 6, 10, 16, 7, 23, 30, 53, 83, 136, 219, 355, 574, 929, 1503, 2432, 3935, 6367, 10302, 16669, 26971, 43640, 70611, 114251, 184862, 299113, 483975, 783088, 1267063, 2050151, 3317214, 5367365, 8684579, 14051944, 22736523, 36788467, 59524990, 96313457, 155838447, 252151904 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A variant of the sequence A267758 where the relation has to hold for prime numbers rather than for nonsquares. The sequence starts like the Fibonacci sequence up to 144, then restarts with 4 up to 16, then it restarts from 7 and grows very large. LINKS M. F. Hasler, Table of n, a(n) for n = 1..100 FORMULA Empirical g.f.: (1+x-229*x^11-142*x^12-19*x^15) / (1-x-x^2). - Colin Barker, Jan 27 2016 PROG (PARI) {a(n, show=0, is=x->issquare(x), a=[1], L=0, U=[])->while(#aL+1, U=setunion(U, [a[#a]]), L++; while(#U&&U[1]<=L+1, U=U[^1]; L++)); a=concat(a, if(is(a[#a])||#a<2, L+1, a[#a]+a[#a-1]))); if(type(show)=="t_VEC", a, a[#a])} CROSSREFS Sequence in context: A105471 A189722 A023441 * A217737 A023442 A000044 Adjacent sequences:  A268130 A268131 A268132 * A268134 A268135 A268136 KEYWORD nonn AUTHOR M. F. Hasler, Jan 26 2016 STATUS approved

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Last modified October 18 04:46 EDT 2019. Contains 328145 sequences. (Running on oeis4.)