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

1,1

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).

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

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 *)

Prog

From M. F. Hasler, May 24 2009: (Start)
(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

Crossrefs

Cf. A101926, A087965, A074411, A110998, A051861, A048222.

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

Sequence in context: A373731 A263108 A274182 * A097963 A063936 A240914

Adjacent sequences: A139563 A139564 A139565 * A139567 A139568 A139569

Keyword

base,nonn,easy

Author

Robert Gornall (rob(AT)khobbits.net), Jun 11 2008

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

Status

approved