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

0,2

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.

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 *)

Prog

(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)))

Crossrefs

Cf. A013929, A077224, A077225, A085902.

Sequence in context: A080705 A032921 A163785 * A077225 A236526 A039559

Adjacent sequences: A080790 A080791 A080792 * A080794 A080795 A080796

Keyword

nonn

Author

Ralf Stephan, Mar 25 2003

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

Status

approved