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A171250
Row lengths of A082381: number of iterations of "sum of digits squared" until 1 or 4 is reached.
3
1, 1, 11, 1, 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, 9, 3, 7, 10, 5, 2, 4, 14, 4, 10, 4, 6, 11, 4, 8, 12, 3, 4, 12, 1
OFFSET
1,3
COMMENTS
In the spirit of A082381, the map A003132 ("sum of digits squared") is applied at least once to the initial value n; the sequence gives the number of iterations until 1 or 4 is reached.
FORMULA
a(n) = O(log* n).
MATHEMATICA
Table[Length[NestWhileList[Total[IntegerDigits[#]^2]&, n, !MemberQ[{1, 4}, #]&]]-1, {n, 100}]/.(0->1) (* Harvey P. Dale, Jun 08 2017 *)
PROG
(PARI) A171250(n)=my(c=0); until( n==4 || n==1, c++; n=norml2(eval(Vec(Str(n))))); c
CROSSREFS
Cf. A082381, A003132, A082382, A000216 (n=2), A000218 (n=3), A080709 (n=4), A000221 (n=5), A008460 (n=6), A008461 (n=7: ends in 1), A008462 (n=8), A008462 (n=9), A139566 (n=15), A122065 (n=74169), A000012 (n=1).
Sequence in context: A185540 A095193 A374332 * A010201 A228407 A231928
KEYWORD
nonn,base
AUTHOR
M. F. Hasler, Dec 18 2009
EXTENSIONS
Formula from Charles R Greathouse IV, Aug 02 2010
Corrected and extended by Harvey P. Dale, Jun 08 2017
STATUS
approved