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 A092984 a(n) = the least k >= 1 such that n! + k is squarefree. 2
 1, 1, 1, 2, 2, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Conjecture: There exists a finite k such that a(n) < k for all n. Subsidiary sequence: Index of the first occurrence of n in this sequence. In case the conjecture is true, this sequence would be finite. If a(n) = 2 ==> n!+1 is divisible by a square (sequence A064237). - Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 29 2004 LINKS FORMULA a(n) = A092983(n) - n!. EXAMPLE a(5) = 2 = 122 - 5! = 122 - 120 (as 121 = 11^2 is not squarefree). MATHEMATICA Table[SelectFirst[Range@ 10, SquareFreeQ[n! + #] &], {n, 45}] (* Michael De Vlieger, Aug 23 2017 *) PROG (PARI) a(n)=for(i=1, n!, if(issquarefree(n!+i), return(i))) (PARI) A092984(n) = { my(k=1); while(!issquarefree(n!+k), k++); k; }; \\ Antti Karttunen, Aug 22 2017 CROSSREFS Cf. A000142, A064237, A092983. Sequence in context: A324496 A137454 A030613 * A297382 A258257 A086600 Adjacent sequences:  A092981 A092982 A092983 * A092985 A092986 A092987 KEYWORD nonn AUTHOR Amarnath Murthy, Mar 28 2004 EXTENSIONS More terms from Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 29 2004 More terms from David Wasserman, Sep 27 2006 Typo in description corrected by Antti Karttunen, Aug 22 2017 STATUS approved

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Last modified October 21 14:40 EDT 2019. Contains 328301 sequences. (Running on oeis4.)