A139566 a(n) is the sum of squares of digits of a(n-1); a(1)=15.
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
Offset: 1
Links
- Colin Barker, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 1).
Crossrefs
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
Programs
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Mathematica
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 *) -
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)
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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
Formula
Eventually periodic with period 8.
a(n) = A008463(n) for n > 4. - M. F. Hasler, May 24 2009
a(n) = a(n-8) for n > 11. - Colin Barker, Aug 24 2015
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
Extensions
More terms from Stefan Steinerberger, Jun 14 2008
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
Comments