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, 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

Offset: 1

Author

M. F. Hasler, Jan 26 2016

Keywords

• nonn

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

Programs

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])}

Formula

Empirical g.f.: (1+x-229*x^11-142*x^12-19*x^15) / (1-x-x^2). - Colin Barker, Jan 27 2016