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 A008462 Take sum of squares of digits of previous term; start with 8. 14
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 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). 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) 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 *) PROG (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 (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 (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 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 Sequence in context: A137664 A317028 A014392 * A043078 A037413 A107626 Adjacent sequences: A008459 A008460 A008461 * A008463 A008464 A008465 KEYWORD nonn,base,easy AUTHOR N. J. A. Sloane STATUS approved

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Last modified June 17 15:57 EDT 2024. Contains 373463 sequences. (Running on oeis4.)