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

Author

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

Keywords

• base
• nonn
• easy

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. 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

Programs

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)

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