A084759 -id:A084759 - cp's OEIS frontend

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

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

nonn

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

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

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

Cf. A084759, A121862.

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 *)

More terms from David Wasserman, Jan 05 2005
Definition corrected by Zak Seidov, Nov 01 2011
Definition corrected by Zak Seidov, Feb 11 2015

A084760 Squarefree numbers in ascending order such that the difference of successive terms is unique. a(m) - a(m-1) = a(k) - a(k-1) iff m = k.

Original entry on oeis.org

2, 3, 5, 10, 13, 17, 23, 30, 38, 47, 57, 69, 82, 93, 107, 122, 138, 155, 173, 193, 214, 233, 255, 278, 302, 327, 353, 381, 410, 437, 467, 498, 530, 563, 597, 633, 670, 705, 743, 782, 822, 863, 905, 949, 994, 1037, 1085, 1131, 1178, 1227, 1277, 1329, 1382, 1433

Offset: 1

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

nonn

The sequence of first differences is 1, 2, 5, 3, 4, 6, 7, 8, 9, 10, 12, 13, 11, 14, 15, 16, 17, 18, 20, 21, 19, ... Conjecture: (1) every number is a term of this sequence. For every number r there exists some k such that a(k) - a(k-1) = r. Question: What is the longest string of consecutive integers in this sequence (of successive differences)?

Answer: 5, as exemplified by the 6 values 17 to 57. Any longer series with differences consecutive integers must include a multiple of 4, as can be seen by enumerating all possibilities modulo 4. - Franklin T. Adams-Watters, Jul 14 2006

			After 5 the next term is 10 and not 6 or 7, as 6-5 = 3-2 =1 and 7-5 = 5-3 = 2.

Cf. A005117, A084758, A084759.

More terms from Franklin T. Adams-Watters, Jul 14 2006

cp's OEIS Frontend

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

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