A077225 Starting with a(0) = 1, smallest squarefree number k such that, for all a(m), m < n, k + a(m) is not squarefree.
1, 3, 15, 17, 233, 291, 577, 723, 1455, 3615, 8117, 8835, 9505, 30833, 128773, 130827, 239595, 273435, 426891, 654135, 676297, 926117, 1455533, 1662533, 2389517, 2762427, 2820927, 7994449, 8098527, 14319073, 16766835, 20506733, 27606617, 31627817, 43558023, 55566015
Offset: 0
Keywords
Examples
17 belongs to this sequence as 17 + 1, 17 + 3, 17 + 15 all are divisible by some square.
Programs
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Mathematica
a[0] = 1; a[n_] := a[n] = Module[{t = Array[a, n, 0], k = a[n - 1] + 1}, While[! SquareFreeQ[k] || AnyTrue[t, SquareFreeQ[k + #] &], k++]; k]; Array[a, 20, 0] (* Amiram Eldar, Aug 21 2023 *) -
PARI
v=vector(60); v[1]=1; print1("1,");for(n=2,60, for(k=1,10^15,if(issquarefree(k),s=0;for(l=1,n-1,if(issquarefree(k+v[l]),break);s=s+1)); if(s==n-1,print1(k",");v[n]=k;break)))
Extensions
Edited by Ralf Stephan, Mar 25 2003
More terms from Sam Alexander, Dec 12 2003
a(22) corrected and a(33)-a(35) added by Amiram Eldar, Aug 21 2023