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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(#a<n, show&&if(type(show)=="t_STR", write(show, #a, " ", a[#a]), print1(a[#a]", ")); if(a[#a]>L+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.)