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

Author

Henry Bottomley, Apr 28 2000

Keywords

• base
• nice
• nonn

Examples

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

Links

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

Crossrefs

Cf. A000217.

Programs

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 *)