A338845 No nonprime digit is present in a(n) * a(n+1).

1, 2, 11, 3, 9, 8, 4, 13, 21, 12, 6, 37, 15, 5, 7, 36, 62, 86, 27, 101, 22, 16, 17, 19, 28, 84, 33, 69, 83, 31, 25, 23, 14, 18, 29, 77, 49, 48, 74, 78, 94, 38, 194, 378, 199, 127, 175, 43, 54, 143, 39, 57, 41, 55, 61, 53, 44, 58, 134, 248, 224, 123, 45, 75, 47, 59, 97, 26, 202, 161, 157, 46, 82, 271, 87, 256

Offset: 1

Author

Eric Angelini and Carole Dubois, Nov 11 2020

Keywords

• base
• nonn

Comments

The nonprime digits are 0, 1, 4, 6, 8 and 9. This is the lexicographically earliest sequence of distinct positive terms with this property.

Examples

			a(1) * a(2) = 1 * 2 = 2 (no nonprime digit is present);
a(2) * a(3) = 2 * 11 = 22 (no nonprime digit is present);
a(3) * a(4) = 11 * 3 = 33 (no nonprime digit is present);
a(4) * a(5) = 3 * 9 = 27 (no nonprime digit is present); etc.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..6500

Crossrefs

Cf. A338839, A338840, A338841, A338842, A338843, A338844, A338846 (variants on the same idea).

Programs

Maple

N:= 500: # for terms before the first term >= N
S:= select(t -> t mod 10 <> 0, [$2...N]):
nS:= nops(S):
V:=Vector(N):
V[1]:= 1:
for n from 2 do
  for i from 1 to nS+2-n do
    s:= S[i];
    if convert(convert(V[n-1]*s,base,10),set) subset {2,3,5,7} then
      V[n]:= s;
      S:= subsop(i=NULL,S);
      break
    fi;
  od;
  if V[n] = 0 then break fi;
od:
convert(V[1..n-1],list); # Robert Israel, Nov 18 2020

Mathematica

Block[{a = {1}}, Do[Block[{k = 1}, While[Nand[FreeQ[a, k], NoneTrue[IntegerDigits@ Total[a[[-1]]*k], ! PrimeQ@ # &]], k++]; AppendTo[a, k]], {i, 2, 76}]; a] (* Michael De Vlieger, Nov 12 2020 *)