A338846 No nonprime digit is present in a(n) + a(n+1).

0, 2, 1, 4, 3, 19, 6, 16, 7, 15, 8, 14, 9, 13, 10, 12, 11, 21, 31, 22, 5, 17, 18, 34, 23, 29, 24, 28, 25, 27, 26, 46, 176, 47, 30, 42, 33, 20, 32, 40, 35, 37, 36, 39, 38, 184, 41, 181, 44, 178, 45, 177, 48, 174, 49, 173, 50, 172, 51, 171, 52, 170, 53, 169, 54, 168, 55, 167, 56, 166, 57, 165, 58, 164, 59

Offset: 1

Author

Eric Angelini and Carole Dubois, Nov 11 2020

Keywords

• base
• nonn
• look

Comments

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

Examples

			a(1) + a(2) = 0 + 2 = 2 (no nonprime digit is present);
a(2) + a(3) = 2 + 1 = 3 (no nonprime digit is present);
a(3) + a(4) = 1 + 4 = 5 (no nonprime digit is present);
a(4) + a(5) = 4 + 3 = 7 (no nonprime digit is present);
a(5) + a(6) = 3 + 19 = 22 (no nonprime digit is present); etc.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Index entries for sequences that are permutations of the nonnegative integers

Crossrefs

Cf. A338839, A338840, A338841, A338842, A338843, A338844, A338845 (variants on the same idea).

Programs

Maple

N:= 1000: # for terms before the first term > N
S:= [$1...N]:
V:=Vector(N):
for n from 2 to N do
  for i from 1 to N+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 = {0}}, Do[Block[{k = 1}, While[Nand[FreeQ[a, k], NoneTrue[IntegerDigits@ Total[a[[-1]] + k], ! PrimeQ@ # &]], k++]; AppendTo[a, k]], {i, 2, 75}]; a] (* Michael De Vlieger, Nov 12 2020 *)