

A084758


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


26



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
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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(k1) = 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 2923= 115 =6, 3123 = 1911=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



