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Search: id:A053699
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| A053699 |
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a(n) = n^4+n^3+n^2+n+1. |
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+0
29
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| 1, 5, 31, 121, 341, 781, 1555, 2801, 4681, 7381, 11111, 16105, 22621, 30941, 41371, 54241, 69905, 88741, 111151, 137561, 168421, 204205, 245411, 292561, 346201, 406901, 475255, 551881, 637421, 732541, 837931, 954305, 1082401, 1222981
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OFFSET
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0,2
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COMMENT
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a(n) = 11111 in base n.
Let Phi_k(x) be the k-th cyclotomic polynomial and form the sequence Phi_k(0), Phi_k(1), Phi_k(2), ... This gives A000027 (k=2), A002061 (k=3), A002522 (k=4), A053699 (k=5), A002061 (k=6), A053716 (k=7), A002523 (k=8), A060883 (k=9), A060884 (k=10), A060885 (k=11), A060886 (k=12), A060887 (k=13), A060888 (k=14), A060889 (k=15), A060890 (k=16), A060891 (k=18), A060892 (k=20), A060893 (k=24), A060894 (k=30), A060895 (k=32), A060896 (k=36).
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FORMULA
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a(n) =n^4+n^3+n^2+n+1 =(n^5-1)/(n-1)
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EXAMPLE
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a(3)=121 because 11111 base 3 =81+27+9+3+1=121
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CROSSREFS
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Adjacent sequences: A053696 A053697 A053698 this_sequence A053700 A053701 A053702
Sequence in context: A024399 A099083 A096944 this_sequence A152122 A041303 A077719
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KEYWORD
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nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Mar 23 2000
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