A338844 No prime digits are present in a(n) * a(n+1).

0, 1, 4, 2, 3, 6, 8, 5, 12, 7, 13, 32, 14, 10, 9, 11, 18, 23, 20, 22, 19, 26, 16, 25, 24, 17, 38, 28, 30, 27, 33, 36, 29, 21, 39, 49, 34, 35, 40, 15, 44, 41, 46, 88, 50, 80, 51, 91, 54, 37, 53, 77, 52, 79, 59, 71, 58, 70, 63, 78, 57, 72, 62, 97, 67, 73, 56, 74, 60, 31, 48, 85, 76, 55, 112, 43, 42, 45

Offset: 1

Author

Eric Angelini and Carole Dubois, Nov 11 2020

Keywords

• nonn
• look
• base

Comments

The prime digits are 2, 3, 5 and 7. 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 * 1 = 0 (no prime digit is present);
a(2) * a(3) = 1 * 4 = 4 (no prime digit is present);
a(3) * a(4) = 4 * 2 = 8 (no prime digit is present);
a(4) * a(5) = 2 * 3 = 6 (no prime digit is present);
a(5) * a(6) = 3 * 6 = 18 (no prime digit is present); etc.
		

Links

• Carole Dubois, Table of n, a(n) for n = 1..5000
• Index entries for sequences that are permutations of the nonnegative integers

Crossrefs

Cf. A202268 (no prime digits).

Cf. A338839, A338840, A338841, A338842, A338843, A338845, A338846 (variants on the same idea).

Programs

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, 78}]; a] (* Michael De Vlieger, Nov 12 2020 *)