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A256062 a(1) = 1; for n>1, a(n) = smallest number > a(n-1) such that the pairwise differences of elements are distinct, and for 1<m<n, a(m) does not divide a(n). 1
1, 2, 5, 7, 17, 31, 39, 59, 99, 143, 179, 229, 293, 339, 409, 541, 597, 659, 761, 869, 1013, 1087, 1269, 1369, 1583, 1821, 2007, 2161, 2267, 2609, 2687, 2879, 3123, 3567, 3869, 4073, 4483, 4659, 5181, 5417, 5857, 6243, 6291, 6589, 7387, 7613, 7747, 8433, 8763, 9599, 9727, 10231, 11047, 11513, 12111, 12779, 13491, 14269, 14913 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..59.

EXAMPLE

39 and 99 occur in this sequence as 39 has factors 3 and 13, which are not members, while 99 has factors 3 and 11, but 39 is not a factor of 99.  Also, the pairwise differences are 1, 3, 4, 2, 5, 6, 10, 12, 15, 16, for the members 1 to 17, the next available integer is 24, but it is divisible by 2, 25 is divisible by 5, 27 has difference 10, etc, until we reach 31.  14, 24, 26, 29 and 30 are new differences to avoid, and 39 becomes a(7).

MATHEMATICA

count=2; seq=Table[1, {a, 1, 3000000}]; nonarth=seq; nonarth[[1]]=1; nonarth[[2]]=2; nonarth=DeleteDuplicates[Flatten[Sort[nonarth]]]; arthcnt=Length[nonarth]; diffs=seq; diffs[[1]]=1; diffs=DeleteDuplicates[diffs]; tmpdiffs=seq; diffcnt=1; arthcnt=2; move=0; test=nonarth[[count]]+1; Parallelize[While[count<=500, a=1; While[And[a<=arthcnt, move==0], tmpdiffs[[a]]=Abs[test-onarth[[a]]]; If[And[a>1, Mod[test, nonarth[[a]]]==0], move++]; If[MemberQ[diffs, tmpdiffs[[a]]], move++]; a++; ]; If[move==0, PrependTo[nonarth, test]; nonarth=DeleteDuplicates[Flatten[Sort[nonarth]]]; arthcnt=Length[nonarth]; count++; test++; PrependTo[diffs, tmpdiffs]; diffs=DeleteDuplicates[Flatten[Sort[diffs]]]; If[Length[diffs]>3000000, count=501, diffcnt=Length[diffs]]; tmpdiffs=seq; , move=0; tmpdiffs=seq; test++; ]; ]; ];

CROSSREFS

A005282 is pairwise distinct difference, and this sequence restricts divisors.

Sequence in context: A066039 A142341 A318731 * A303677 A303802 A045357

Adjacent sequences:  A256059 A256060 A256061 * A256063 A256064 A256065

KEYWORD

nonn

AUTHOR

Christopher Brice Turner, Mar 13 2015

STATUS

approved

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Last modified February 16 02:39 EST 2019. Contains 320140 sequences. (Running on oeis4.)