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

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

Author

N. J. A. Sloane, Mira Bernstein

Keywords

• nonn
• base

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.

Crossrefs

Cf. A000216, A000218, A300081, etc.

Cf. A003132.

Programs

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 *)

Formula

a(n) = 0 if n = 1 or 4, otherwise a(n) = 1 + a(A003132(n)). - Robert Israel, Apr 11 2019