A084758 The slowest increasing sequence of primes such that difference of successive terms is unique.

2, 3, 5, 11, 19, 23, 37, 47, 59, 79, 97, 113, 137, 163, 191, 223, 257, 293, 331, 353, 383, 431, 487, 541, 587, 631, 673, 733, 773, 823, 881, 947, 1009, 1061, 1129, 1193, 1277, 1367, 1439, 1531, 1601, 1697, 1777, 1871, 1949, 2053, 2129, 2203, 2309, 2411, 2521

Offset

1,1

Comments

The sequence of successive differences is 1,2,6,8,4,14,10,12,20,18,16,... Conjecture: every even number is a term of this sequence. For every even number e there exists some k such that a(k) - a(k-1) = e.

The slowest increasing sequence of primes such that each difference between successive terms is unique. - Zak Seidov, Feb 10 2015

Links

Zak Seidov, Table of n, a(n) for n = 1..1000

Example

After 23, the next term is 37 and not 29 or 31 as 29-23= 11-5 =6, 31-23 = 19-11=8.

Mathematica

diffs = {}; prms = {2}; p = 2; Do[While[p = NextPrime[p]; d = p - prms[[-1]]; MemberQ[diffs, d]]; AppendTo[diffs, d]; AppendTo[prms, p], {100}]; prms (* T. D. Noe, Nov 01 2011 *)

Crossrefs

Cf. A084759, A121862.

Sequence in context: A024371 A344963 A231479 * A087582 A235661 A070865

Adjacent sequences: A084755 A084756 A084757 * A084759 A084760 A084761

Keyword

nonn

Author

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

Extensions

More terms from David Wasserman, Jan 05 2005

Definition corrected by Zak Seidov, Nov 01 2011

Definition corrected by Zak Seidov, Feb 11 2015

Status

approved