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

Author

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

Keywords

• nonn

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

Examples

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

Links

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

Crossrefs

Cf. A084759, A121862.

Programs

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 *)

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