A008462 Take sum of squares of digits of previous term; start with 8.

8, 64, 52, 29, 85, 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, 58, 89, 145

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• base
• easy

References

• R. Honsberger, Ingenuity in Math., Random House, 1970, p. 83.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..100
• Arthur Porges, A set of eight numbers, Amer. Math. Monthly 52 (1945), 379-382.
• 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), A008463 (starting with 9), A139566 (starting with 15), A122065 (starting with 74169). - M. F. Hasler, May 24 2009

Programs

Magma

[8, 64, 52, 29, 85] cat &cat[[89, 145, 42, 20, 4, 16, 37, 58]: n in [0..17]]; // Vincenzo Librandi, Jan 29 2013

Mathematica

NestList[Total[IntegerDigits[#]^2]&, 8, 80] (* Vincenzo Librandi, Jan 29 2013 *)
PadRight[{8,64,52,29,85},80,{20,4,16,37,58,89,145,42}] (* Harvey P. Dale, Dec 27 2019 *)

PARI

A008462(n)=[8, 64, 52, 29, 85, 89, 145, 42, 20, 4, 16, 37, 58][if(n>13,(n-6)%8+6,n)] \\ M. F. Hasler, May 24 2009

PARI

Vec(x*(8 + 64*x + 52*x^2 + 29*x^3 + 85*x^4 + 89*x^5 + 145*x^6 + 42*x^7 + 12*x^8 - 60*x^9 - 36*x^10 + 8*x^11 - 27*x^12) / ((1 - x)*(1 + x)*(1 + x^2)*(1 + x^4)) + O(x^60)) \\ Colin Barker, Apr 28 2018

Formula

Periodic with period 8.

a(n) = A080709(n-1) for n >= 5 and a(n) = A000221(n-1) = A008460(n+4) for all n >= 4. - M. F. Hasler, May 24 2009; edited and extended Apr 27 2018

From Colin Barker, Apr 28 2018: (Start)

G.f.: x*(8 + 64*x + 52*x^2 + 29*x^3 + 85*x^4 + 89*x^5 + 145*x^6 + 42*x^7 + 12*x^8 - 60*x^9 - 36*x^10 + 8*x^11 - 27*x^12) / ((1 - x)*(1 + x)*(1 + x^2)*(1 + x^4)).

a(n) = a(n-8) for n>13.

(End)