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

1,3

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.

Links

Carole Dubois, Table of n, a(n) for n = 1..5000

Index entries for sequences that are permutations of the nonnegative integers

Example

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.

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 *)

Crossrefs

Cf. A202268 (no prime digits).

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

Sequence in context: A282865 A241051 A275590 * A333406 A083181 A134074

Adjacent sequences: A338841 A338842 A338843 * A338845 A338846 A338847

Keyword

nonn,look,base

Author

Eric Angelini and Carole Dubois, Nov 11 2020

Status

approved