A309123 a(1) = 50 and for any n > 0, a(n+1)^2 is the smallest square that begins with a(n).

50, 71, 267, 517, 2274, 1508, 3884, 1971, 444, 667, 817, 286, 535, 732, 856, 2926, 541, 736, 858, 293, 542, 233, 483, 695, 834, 2888, 16995, 41225, 20304, 4506, 6713, 2591, 5091, 22564, 47502, 21795, 46686, 21607, 46484, 215602, 46433, 68142, 261041, 510922

Offset: 1

Author

Rémy Sigrist, Jul 13 2019

Keywords

• nonn
• base

Comments

This sequence is similar to A308055.

The initial value (50) seems to be the first one for which the iteration of A018796 diverges; there are neither duplicates nor squares among the first 79000 terms.

Examples

			The first terms, alongside the square of a(n+1), are:
  n   a(n)  a(n+1)^2
  --  ----  --------
   1    50      5041
   2    71     71289
   3   267    267289
   4   517   5171076
   5  2274   2274064
   6  1508  15085456
   7  3884   3884841
   8  1971    197136
   9   444    444889
  10   667    667489
  11   817     81796
  12   286    286225
  13   535    535824
  14   732    732736
  15   856   8561476
  16  2926    292681
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..1000
• Rémy Sigrist, PARI program for A309123

Crossrefs

Cf. A018796, A308055.

Programs

PARI

See Links section.

Formula

a(1) = 50 and then a(n+1) = A018796(a(n)) for n > 0.