

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.


5



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
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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



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:


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



KEYWORD



AUTHOR



STATUS

approved



