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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
Arthur Porges, A set of eight numbers, Amer. Math. Monthly 52 (1945), 379-382.
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
KEYWORD
nonn,base,easy
AUTHOR
STATUS
approved

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