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%I #21 Jul 25 2020 18:38:21
%S 1,0,0,3,0,2,0,2,2,1,0,1,0,2,2,1,0,1,0,6,1,5,0,4,2,3,1,5,0,6,0,2,5,1,
%T 2,4,0,1,3,4,0,4,0,3,2,3,0,2,1,5,2,2,0,1,4,1,4,3,0,3,0,3,3,3,1,2,0,2,
%U 4,4,0,1,0,2,4,1,3,3,0,4,1,3,0,2,3,2,2
%N Start with n; add to it any of its digits; repeat; a(n) = minimal number of steps needed to reach a prime.
%C a(n) = 0 iff n is a prime.
%C Is it a theorem that a(n) always exists?
%C Yes: the proof is similar to that of _Robert Israel_ for A241180. - _Rémy Sigrist_, Jul 25 2020
%D Eric Angelini, Posting to Sequence Fans Mailing List, Apr 20 2014
%H Hiroaki Yamanouchi, <a href="/A241181/b241181.txt">Table of n, a(n) for n = 1..100000</a>
%e Examples, in condensed notation:
%e 1+1=2
%e 2
%e 3
%e 4+4=8+8=16+1=17
%e 5
%e 6+6=12+1=13
%e 7
%e 8+8=16+1=17
%e 9+9=18+1=19
%e 10+1=11
%e 11
%e 12+1=13
%e 13
%e 14+4=18+1=19
%e 15+1=16+1=17
%e 16+1=17
%e 17
%e 18+1=19
%e 19
%e 20+2=22+2=24+2=26+6=32+2=34+3=37
%e ...
%t A241181[n_] := Module[{c, nx},
%t If[PrimeQ[n], Return[0]];
%t c = 1; nx = n;
%t While[ ! AnyTrue[nx = Flatten[nx + IntegerDigits[nx]], PrimeQ], c++];
%t Return[c]];
%t Table[A241181[i], {i, 100}] (* _Robert Price_, Mar 17 2019 *)
%Y Related sequences: A241173, A241174, A241175, A241176, A241177, A241178, A241179, A241180, A241181, A241182, A241183.
%K easy,nonn,base
%O 1,4
%A _N. J. A. Sloane_, Apr 23 2014
%E a(23)-a(87) from _Hiroaki Yamanouchi_, Sep 05 2014