A003621 Number of iterations until n reaches 1 or 4 under x goes to sum of squares of digits map. (Formerly M4764)

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

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

Adjacent sequences: A003618 A003619 A003620 * A003622 A003623 A003624

Keyword

nonn,base

Author

N. J. A. Sloane, Mira Bernstein

Status

approved