A255892 Primes p such that each decimal digit of p is equal to the difference of two other digits of p.

101, 10111, 10133, 10177, 10313, 10331, 10771, 11909, 13103, 14401, 16061, 17107, 20233, 20323, 20929, 22303, 23203, 29209, 30113, 30223, 30553, 30773, 31013, 32203, 34403, 35053, 37307, 38083, 38803, 40343, 40433, 40499, 40949, 43403, 44101, 44909, 47407

Offset

1,1

Comments

Let x(1)x(2)...x(q-1)x(q) denote the decimal expansion of a prime number p. The sequence lists the primes p such that, for each index i, x(i) = x(u) - x(v) for some indices u and v.

Subsequence of A255966.

Each term of the sequence contains at least two identical decimal digits and at least one 0 digit.

The number 112345678909 is the smallest element of the sequence containing 10 distinct digits.

Number of terms < 10^n: 0, 0, 1, 1, 64, 1100, 20799, 340324, ... . - Robert G. Wilson v, Mar 10 2015

Links

Michel Lagneau, Table of n, a(n) for n = 1..10000

Example

101 is in the sequence because 1 = 1 - 0 and 0 = 1 - 1.

Maple

for n from 100 to 100000 do:
  x:=convert(n, base, 10):n1:=nops(x):c:=0:T:=array(1..n1-1):
    for nn from 1 to n1 do:
     z:=x[nn]:
     k:=0:
      for j from 1 to n1 do:
       if nn<>j
       then
       k:=k+1:T[k]:=x[j]:
       else
       fi:
      od:
      ii:=0:
        for a from 1 to n1-1 while(ii=0) do:
         for b from a+1 to n1-1 while(ii=0) do:
         if z=abs(T[a]-T[b]) then ii:=1:c:=c+1:
         else
         fi:
        od:od:
      od:
      if c=n1 and type(n, prime)=true then printf(`%d, `, n):
      else
      fi:
  od:

Mathematica

fQ[n_] := Block[{id = IntegerDigits@ n, lng = 1 + Floor@ Log10@ n}, Union@ Table[c = Complement[ Range@ lng, {i}]; MemberQ[ Union@ Flatten@ Table[ Abs[id[[j]] - id[[k]]], {j, c}, {k, c}], id[[i]]], {i, lng}] == {True}]; Select[ Prime@ Range@ 5000, fQ] (* Robert G. Wilson v, Mar 10 2015 *)

Crossrefs

Cf. A000040, A255893, A255917, A255966.

Sequence in context: A094028 A144564 A261965 * A065074 A113628 A135375

Adjacent sequences: A255889 A255890 A255891 * A255893 A255894 A255895

Keyword

nonn,base

Author

Michel Lagneau, Mar 09 2015

Status

approved