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A275604
The concatenation of a(n) and |a(n)-a(n+1)| is prime and all such concatenations are different one from another. Terms are distinct.
2
1, 2, 5, 8, 11, 14, 23, 12, 19, 6, 7, 4, 3, 10, 9, 16, 13, 20, 31, 24, 25, 18, 17, 26, 29, 32, 15, 22, 35, 38, 41, 30, 37, 28, 27, 34, 21, 50, 39, 46, 43, 40, 49, 48, 55, 36, 53, 76, 33, 52, 51, 64, 57, 56, 47, 68, 45, 58, 65, 44, 67, 60, 59, 62, 73, 42, 61, 54, 71, 80, 63, 74, 77, 94, 75, 82, 79, 72, 83, 66
OFFSET
1,2
COMMENTS
The sequence starts with a(1) = 1 and is always extended with the smallest integer not yet present that does not lead to a contradiction.
This sequence is conjectured to be a permutation of the positive integers and is a variant of A275603 that shares with it the first 174 terms.
LINKS
EXAMPLE
1,2,5,8,11,14,23,12,19,6,7,
|1-2| = 1 and 11 is prime; |2-5| = 3 and 23 is prime; |5-8| = 3 and 53 is prime; |8-11| = 3 and 83 is prime; |11-14| = 3 and 113 is prime; etc.
MATHEMATICA
a = {1}; Do[k = 1; While[Or[! PrimeQ@ FromDigits[IntegerDigits[a[[i - 1]]]~Join~IntegerDigits[Abs[a[[i - 1]] - k]]], MemberQ[a, k]], k++]; AppendTo[a, k], {i, 2, 80}]; a (* Michael De Vlieger, Nov 14 2016 *)
CROSSREFS
Cf. A275603.
Sequence in context: A287960 A102795 A275603 * A173698 A162938 A356447
KEYWORD
nonn,base
AUTHOR
STATUS
approved