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 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. 11
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified November 19 00:12 EST 2019. Contains 329310 sequences. (Running on oeis4.)