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

0,2

Links

Table of n, a(n) for n=0..35.

Example

17 belongs to this sequence as 17 + 1, 17 + 3, 17 + 15 all are divisible by some square.

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 *)

Prog

(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)))

Crossrefs

Cf. A013929, A077224, A080793, A085902.

Sequence in context: A032921 A163785 A080793 * A236526 A039559 A045753

Adjacent sequences: A077222 A077223 A077224 * A077226 A077227 A077228

Keyword

nonn

Author

Amarnath Murthy, Nov 03 2002

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

Status

approved