A094830 Start with x = n, repeatedly replace x with x + sum of squares of digits of x until you reach a prime; sequence gives number of steps.

1, 0, 0, 6, 0, 4, 0, 11, 5, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 5, 13, 9, 0, 4, 11, 12, 17, 3, 0, 8, 0, 8, 7, 1, 7, 3, 0, 5, 7, 4, 0, 3, 0, 3, 7, 8, 0, 2, 2, 2, 6, 3, 0, 10, 2, 3, 1, 3, 0, 3, 0, 2, 2, 18, 2, 11, 0, 2, 6, 9, 0, 10, 0, 1, 1, 2, 5, 1, 0, 16, 2, 8, 0, 3, 11, 6, 10, 2, 0, 4, 1, 15, 2, 1, 9, 2, 0, 7, 7, 1

Offset

1,4

Comments

It is currently not known if this sequence is well defined, i.e. if for all n>=1 there exists an integer v such that a(n) = v. If the sequence is not well defined then the given programs are incorrect as they will get stuck in an infinite loop for some integers. - Peter Luschny, Oct 28 2016

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(4)=6 because 4 -> 20 -> 24 -> 44 -> 76 -> 161 -> 199, takes 6 steps to reach a prime.

Maple

f:= proc(n) local x, k;
x:= n;
for k from 0 do
  if isprime(x) then return k fi;
  x:= x + add(t^2, t = convert(x, base, 10))
od;
end proc:
map(f, [$1..100]); # Robert Israel, Oct 27 2016

Mathematica

p[n_]:=Length[NestWhileList[#+Total[IntegerDigits[#]^2]&, n, !PrimeQ[ #]&]]-1; Array[p, 100] (* Harvey P. Dale, Dec 03 2011 *)

Prog

(PARI) a(n) = my(k=0); while(!isprime(n), d=digits(n); n+=vecsum(vector(#d, i, d[i]^2)); k++) ; k \\ David A. Corneth, Oct 27 2016

Crossrefs

Cf. A003132, A094877.

Sequence in context: A089841 A202542 A019766 * A196878 A209835 A344973

Adjacent sequences: A094827 A094828 A094829 * A094831 A094832 A094833

Keyword

base,easy,nonn,look

Author

Jason Earls, Jun 13 2004

Status

approved