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A051442
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a(n) = n^(n+1)+(n+1)^n.
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13
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1, 3, 17, 145, 1649, 23401, 397585, 7861953, 177264449, 4486784401, 125937424601, 3881436747409, 130291290501553, 4731091158953433, 184761021583202849, 7721329860319737601, 343809097055019694337, 16248996011806421522977
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OFFSET
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0,2
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COMMENTS
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Odd prime p divides a(p-2). For n>1, a(prime(n)-2)/prime(n) = A125074(n) = {1, 29, 3343, 407889491, 298572057493, 454195874136455153, ...}. Prime p divides a((p+5)/2) for p = {19, 23, 61}. - Alexander Adamchuk, Nov 18 2006
For all n != 1, a(n) mod 8 = 1.
If n mod 6 = 0, 3, or 5, then a(n) mod 6 = 1. If n mod 6 = 1, then a(n) mod 6 = 3. If n mod 6 = 2 or 4, then a(n) mod 6 = 5.
For all n, a(n)-1 is a multiple of n^2.
For n odd and n >= 3, a(n)-1 is a multiple of (n+1)^2.
For n even and n >= 0, a(n)+1 is a multiple of (n+1)^2.
For proofs, see the Englander link. (End)
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LINKS
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FORMULA
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a(n) = a(n-1) + A258389(n) for n >= 1.
(End)
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MATHEMATICA
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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