A054048 Earliest sequence with a(a(n)) = n*(n+1)/2 (Triangular numbers).

0, 1, 4, 10, 3, 7, 55, 15, 9, 36, 6, 12, 66, 14, 91, 28, 17, 136, 19, 171, 22, 1540, 210, 24, 276, 26, 325, 29, 120, 378, 31, 465, 33, 528, 35, 595, 45, 38, 703, 40, 780, 42, 861, 44, 946, 666, 47, 1081, 49, 1176, 51, 1275, 53, 1378, 56, 21, 1485, 58, 1653

Offset

0,3

Links

Table of n, a(n) for n=0..58.

Index entries for sequences of the a(a(n)) = 2n family

Example

a(a(3)) = a(10) = 6 = 3*4/2.

Mathematica

nmax = 58; amax = 2000; tri[n_] := n*(n+1)/2; triQ[n_] := triQ[n] = Resolve[ Exists[ k, Reduce[ k > 0 && n == tri[k], k, Integers] ] ]; t = {{0, a[0] = 0}, {1, a[1] = 1}, {2, a[2]}}; While[ !FreeQ[t, a], t = Table[ {n, a[n]}, {n, 0, nmax}]; n = Select[t, !IntegerQ[#[[2]]]& , 1][[1, 1]]; t2 = Union[ Flatten[ Append[ Select[ t, IntegerQ[ #[[2]] ] & ], n] ] ]; an = If[ n == 2, 4, Select[ Complement[ Range[ Max[t2] ], t2], !triQ[#]&, 1][[1]]]; a[n] = an; While[ an < amax, an = a[n = an] = tri[n] ] ]; A054048 = Table[ a[n], {n, 0, nmax}] (* Jean-François Alcover, Jan 05 2012 *)

Crossrefs

Cf. A000217.

Sequence in context: A244152 A070261 A367029 * A121512 A291527 A010715

Adjacent sequences: A054045 A054046 A054047 * A054049 A054050 A054051

Keyword

base,nice,nonn

Author

Henry Bottomley, Apr 28 2000

Status

approved