A306375 Lexicographically earliest sequence starting with a(1) = 12 with no duplicate terms such that [a(n) - (the n-th digit of the sequence)] is prime.

12, 4, 6, 8, 10, 3, 2, 5, 7, 16, 9, 14, 11, 20, 18, 15, 24, 30, 13, 17, 32, 19, 38, 22, 21, 23, 26, 29, 42, 34, 44, 36, 40, 25, 48, 28, 46, 27, 31, 33, 39, 54, 43, 50, 45, 35, 49, 52, 41, 55, 56, 47, 51, 57, 62, 37, 63, 53, 61, 58, 65, 67, 69, 75, 71, 59, 73, 60, 64, 68, 70, 74, 76, 80, 66, 77, 83, 82, 72, 79, 87, 78, 86, 84

Offset

1,1

Comments

Any a(1) < 12 would be in contradiction with the definition.

Links

Jean-Marc Falcoz, Table of n, a(n) for n = 1..20001

Example

The sequence starts with 12,4,6,8,10,3,2,5,7,16,9,14,11,20,18,15,...
a(1) = 12 and [12 - 1 (the 1st digit of the sequence)] = 11 (prime);
a(2) =  4 and [ 4 - 2 (the 2nd digit of the sequence)] = 2 (prime);
a(3) =  6 and [ 6 - 4 (the 3rd digit of the sequence)] = 2;
a(4) =  8 and [ 8 - 6 (the 4th digit of the sequence)] = 2;
a(5) = 10 and [10 - 8 (the 5th digit of the sequence)] = 2;
a(6) =  3 and [ 3 - 1 (the 6th digit of the sequence)] = 2;
a(7) =  2 and [ 2 - 0 (the 7th digit of the sequence)] = 2;
a(8) =  5 and [ 5 - 3 (the 8th digit of the sequence)] = 2;
a(9) =  7 and [ 7 - 2 (the 9th digit of the sequence)] = 5 (prime);
etc.

Crossrefs

Cf. A306321 where the same idea is used.

Sequence in context: A079792 A079791 A018812 * A139358 A004477 A328285

Adjacent sequences: A306372 A306373 A306374 * A306376 A306377 A306378

Keyword

base,nonn

Author

Eric Angelini and Jean-Marc Falcoz, Feb 11 2019

Status

approved