A080793 Starting with a(0) = 1, smallest number k > a(n-1) such that, for all a(m) with m < n, k + a(m) is not squarefree.

1, 3, 15, 17, 147, 233, 577, 735, 3615, 4335, 8117, 9505, 10947, 14403, 25215, 30833, 128773, 220647, 251173, 522003, 617547, 770977, 926117, 967335, 1455533, 1662533, 1960215, 2389517, 2469747, 3528147, 4674747, 5556747, 5730135, 5859903, 10892847, 12127647, 15170547

Offset: 0

Author

Ralf Stephan, Mar 25 2003

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000
• C. B. Lacampagne, C. A. Nicol, and J. L. Selfridge, Sets With Non-Squarefree Sums, in: Richard Mollin (ed.), Number Theory: Proceedings of the First Conference of the Canadian Number Theory Association, Held at the Banff Center, Banff, Alberta, April 17-27, 1988, Berlin; New York: W. de Gruyter, 1990, pp. 299-310.

Crossrefs

Cf. A013929, A077224, A077225, A085902.

Programs

Mathematica

a[0] = 1; a[n_] := a[n] = Module[{t = Array[a, n, 0], k = a[n - 1] + 1}, While[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=v[n-1]+1, 10^15, 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

More terms from Lambert Klasen (Lambert.Klasen(AT)gmx.net) and lambert.herrgesell(AT)aschendorff.de, Jul 26 2005

a(33)-a(36) from Amiram Eldar, Aug 21 2023