A084761 A sequence of primes such that (a(n)-a(n-1)) / (a(n-1)-a(n-2)) is a unique integer.

2, 3, 5, 7, 13, 37, 157, 877, 6637, 46957, 530797, 4885357, 61494637, 684196717, 6911217517, 94089508717, 1576120459117, 23806584715117, 468415869835117, 11583647997835117, 211657826301835117, 3412844679165835117, 73838955442173835117, 1904917835280381835117

Offset

1,1

Comments

The sequence of successive difference ratios (a(n)-a(n-1)) / (a(n-1)-a(n-2)) is 2,1,3,4,5,6,8,7,...

Conjecture: every number is a term of this sequence, or for every number r there exists some k such that (a(k)-a(k-1)) / (a(k-1)-a(k-2)) = r.

Question: What is the longest string of consecutive integers in this sequence (of successive differences)?

Links

Table of n, a(n) for n=1..24.

Example

(a(5)-a(4)) / (a(4)-a(3)) = (13-7) / (7-5) = 3. Then it is to be taken care of that this ratio is not 3 for any other set of three successive terms.

Crossrefs

Sequence in context: A052291 A256072 A072826 * A392757 A038965 A295738

Adjacent sequences: A084758 A084759 A084760 * A084762 A084763 A084764

Keyword

nonn

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 17 2003

Extensions

More terms from David Wasserman, Jan 06 2005

Offset corrected and more terms from Sean A. Irvine, May 08 2026

Status

approved