A241180 Start with n; add to it any of its digits; repeat; a(n) = minimal number of steps needed to reach a prime greater than n.

1, 4, 3, 3, 2, 2, 3, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 6, 6, 1, 5, 3, 4, 2, 3, 1, 5, 1, 6, 2, 2, 5, 1, 2, 4, 4, 1, 3, 4, 3, 4, 1, 3, 2, 3, 2, 2, 1, 5, 2, 2, 2, 1, 4, 1, 4, 3, 3, 3, 1, 3, 3, 3, 1, 2, 1, 2, 4, 4, 2, 1, 2, 2, 4, 1, 3, 3, 3, 4, 1, 3, 3, 2, 3, 2, 2

Offset

1,2

Comments

Is it a theorem that a(n) aways exists?

Yes: as long as nonzero digits are used, eventually you reach a number x starting with 10, large enough that there is a prime between x and 3*x/2. All the numbers from x to 3*x/2 start with 1, so if you use the digit 1 you will eventually reach a prime. - Robert Israel, Mar 17 2019

A variant of this (A241181) sets a(n) = 0 if n is already a prime.

References

Eric Angelini, Posting to Sequence Fans Mailing List, Apr 20 2014

Links

Hiroaki Yamanouchi, Table of n, a(n) for n = 1..100000

Example

Examples, in condensed notation:
1+1=2
2+2=4+4=8+8=16+1=17
3+3=6+6=12+1=13
4+4=8+8=16+1=17
5+5=10+1=11
6+6=12+1=13
7+7=14+4=18+1=19
8+8=16+1=17
9+9=18+1=19
10+1=11
11+1=12+1=13
12+1=13
13+3=16+1=17
14+4=18+1=19
15+1=16+1=17
16+1=17
17+1=18+1=19
18+1=19
19+9=28+8=36+3=39+9=48+8=56+5=61
20+2=22+2=24+2=26+6=32+2=34+3=37
...

Maple

g:= proc(n, Nmax) option remember; local L, d, t;
  if isprime(n) then return 0 fi;
  if n > Nmax then return infinity fi;
  L:= convert(convert(n, base, 10), set) minus {0};
  1 + min(seq(procname(n+d), d=L));
end proc:
f:= proc(n, Nmax) local L, d, t;
  L:= convert(convert(n, base, 10), set) minus {0};
  1 + min(seq(g(n+d, Nmax), d=L))
end proc:
map(f, [$1..200], 1000); # Robert Israel, Mar 17 2019

Mathematica

A241180[n_] := Module[{c, nx},
   c = 1; nx = n;
   While[ !
     AnyTrue[nx = Flatten[nx + IntegerDigits[nx]],
      PrimeQ [#] && # > n &], c++];
   Return[c]];
Table[A241180[i], {i, 100}] (* Robert Price, Mar 17 2019 *)

Crossrefs

Related sequences: A241173, A241174, A241175, A241176, A241177, A241178, A241179, A241180, A241181, A241182, A241183.

Sequence in context: A196274 A073871 A120927 * A117323 A016502 A305743

Adjacent sequences: A241177 A241178 A241179 * A241181 A241182 A241183

Keyword

easy,nonn,base

Author

N. J. A. Sloane, Apr 23 2014

Extensions

a(23)-a(87) from Hiroaki Yamanouchi, Sep 05 2014

Status

approved