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A359808
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a(n) is the least prime factor of the alternating factorial n! - (n-1)! + (n-2)! - ... 1! for n > 2; a(1) = a(2) = 1.
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2
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1, 1, 5, 19, 101, 619, 4421, 35899, 79, 3301819, 13, 29, 47, 23, 1226280710981, 53, 47, 2683, 115578717622022981, 8969, 113, 79, 85439, 12203, 59, 1657, 127, 61, 661, 47, 173183, 1117, 83, 4729, 37, 103, 2858548279, 59, 67, 431, 32656499591185747972776747396512425885838364422981
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OFFSET
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1,3
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COMMENTS
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a(n) is the least prime factor of A005165(n) (unless A005165(n) = 1, in which case a(n) = 1).
a(n) = A005165(n) iff n is a term in A001272 or n < 2.
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LINKS
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Jon E. Schoenfield, Table of n, a(n) for n = 1..149
Eric Weisstein's World of Mathematics, Alternating Factorial
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FORMULA
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a(n) = A020639(A005165).
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MAPLE
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b:= proc(n) option remember; `if`(n=0, 0, n!-b(n-1)) end:
a:= n-> `if`(n<3, 1, min(numtheory[factorset](b(n)))):
seq(a(n), n=1..41); # Alois P. Heinz, Jan 13 2023
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MATHEMATICA
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a[n_] := FactorInteger[AlternatingFactorial[n]][[1, 1]];
Table[a[n], {n, 1, 41}] (* Jean-François Alcover, Jan 24 2023 *)
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CROSSREFS
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Cf. A001272, A005165, A020639.
Sequence in context: A146144 A162292 A321875 * A005165 A071828 A280067
Adjacent sequences: A359805 A359806 A359807 * A359809 A359810 A359811
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KEYWORD
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nonn
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AUTHOR
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Jon E. Schoenfield, Jan 13 2023
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STATUS
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approved
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