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A003621 Number of iterations until n reaches 1 or 4 under x goes to sum of squares of digits map.
(Formerly M4764)
13
0, 1, 11, 0, 8, 13, 5, 9, 10, 1, 2, 9, 2, 10, 10, 7, 9, 9, 4, 1, 9, 10, 3, 2, 7, 9, 10, 3, 6, 11, 2, 3, 10, 8, 9, 12, 6, 7, 11, 8, 10, 2, 8, 4, 11, 8, 9, 10, 4, 8, 10, 7, 9, 11, 9, 8, 10, 5, 8, 13, 7, 9, 12, 8, 8, 11, 6, 2, 12, 5, 9, 10, 6, 9, 10, 6, 5, 4, 3, 9 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
REFERENCES
J. Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 13.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)
A. Porges, A set of eight numbers, Amer. Math. Monthly, 52 (1945), 379-382. [Annotated scanned copy]
Arthur Porges, A set of eight numbers, Amer. Math. Monthly 52 (1945), 379-382.
FORMULA
a(n) = 0 if n = 1 or 4, otherwise a(n) = 1 + a(A003132(n)). - Robert Israel, Apr 11 2019
MAPLE
f:= n -> convert(map(t -> t^2, convert(n, base, 10)), `+`):
g:= proc(n) option remember;
if n = 1 or n = 4 then 0 else 1 + procname(f(n)) fi
end proc:
map(g, [$1..100]); # Robert Israel, Apr 11 2019
MATHEMATICA
Table[Length[NestWhileList[Total[IntegerDigits[#]^2]&, n, #!=1&&#!=4&]], {n, 80}]-1 (* Harvey P. Dale, Dec 31 2016 *)
CROSSREFS
Cf. A000216, A000218, A300081, etc.
Cf. A003132.
Sequence in context: A115595 A342123 A187553 * A348006 A338827 A055963
KEYWORD
nonn,base
AUTHOR
STATUS
approved

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Last modified June 17 15:39 EDT 2024. Contains 373458 sequences. (Running on oeis4.)