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A139566
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a(n) is the sum of squares of digits of a(n-1); a(1)=15.
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13
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15, 26, 40, 16, 37, 58, 89, 145, 42, 20, 4, 16, 37, 58, 89, 145, 42, 20, 4, 16, 37, 58, 89, 145, 42, 20, 4, 16, 37, 58, 89, 145, 42, 20, 4, 16, 37, 58, 89, 145, 42, 20, 4, 16, 37, 58, 89, 145, 42, 20, 4, 16, 37, 58, 89, 145, 42, 20, 4, 16, 37, 58, 89, 145, 42, 20, 4, 16, 37
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OFFSET
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1,1
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LINKS
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FORMULA
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Eventually periodic with period 8.
G.f.: x*(36*x^10 + 6*x^9 - 27*x^8 - 145*x^7 - 89*x^6 - 58*x^5 - 37*x^4 - 16*x^3 - 40*x^2 - 26*x - 15) / ((x-1)*(x+1)*(x^2+1)*(x^4+1)). - Colin Barker, Aug 24 2015
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MATHEMATICA
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a = {15}; Do[AppendTo[a, Plus @@ (IntegerDigits[a[[ -1]]]^2)], {70}]; a (* Stefan Steinerberger, Jun 14 2008 *)
NestList[Total[IntegerDigits[#]^2] &, 15, 70] (* or *) PadRight[ {15, 26, 40}, 70, {42, 20, 4, 16, 37, 58, 89, 145}](* Harvey P. Dale, Jan 28 2013 *)
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PROG
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(PARI) /* to check the given terms */
a=[/* paste the terms here */]; a==vector(#a, n, k=if(n>1, A003132(k), 15))
/* to check the following code, use: a==vector(99, n, A139566(n)) */
A139566(n)=[15, 26, 40, 16, 37, 58, 89, 145, 42, 20, 4][if(n>11, (n-4)%8+4, n)] \\ (End)
(PARI) Vec(x*(36*x^10+6*x^9-27*x^8-145*x^7-89*x^6-58*x^5-37*x^4-16*x^3 -40*x^2-26*x-15)/((x-1)*(x+1)*(x^2+1)*(x^4+1)) + O(x^70)) \\ Colin Barker, Aug 24 2015
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CROSSREFS
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Cf. A003132 (the iterated map), A003621, A039943, A099645, A031176, A007770, A000216 (starting with 2), A000218 (starting with 3), A080709 (starting with 4), A000221 (starting with 5), A008460 (starting with 6), A008462 (starting with 8), A008463 (starting with 9), A122065 (starting with 74169). - M. F. Hasler, May 24 2009
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KEYWORD
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base,nonn,easy
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AUTHOR
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Robert Gornall (rob(AT)khobbits.net), Jun 11 2008
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EXTENSIONS
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Terms checked, using the given PARI code, by M. F. Hasler, May 24 2009
Minor edits and starting value added in name by M. F. Hasler, Apr 27 2018
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STATUS
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approved
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