A265155 Integers which are unique starting points for the algorithm described in A090566.

1, 2, 4, 8, 10, 11, 14, 15, 16, 17, 18, 19, 21, 22, 23

Offset

1,2

Comments

Consider the family of integer sequences generated from a starting value b(1) and the rule that each subsequent term is the smallest number greater than the previous term such that the concatenation of the two is a square. Then using

b(1) = a(1) = 1 yields {1, 6, 25, 281, 961, ...} (A090566),

b(1) = a(2) = 2 yields {2, 5, 29, 241, 1809, ...} (A265147),

b(1) = a(3) = 4 yields {4, 9, 61, 504, 4516, ...} (A265148),

b(1) = a(4) = 8 yields {8, 41, 209, 764, 5225, ...} (A265149),

b(1) = a(5) = 10 yields {10, 24, 336, 400, 689, ...} (A265150),

b(1) = a(6) = 11 yields {11, 56, 169, 744, 769, ...} (A265151),

...

Links

Table of n, a(n) for n=1..15.

Example

The complement of {a(n)} is {3, 5, 6, 7, 9, 12, 13, 20, ...}; using any of these values as b(1) yields a sequence that quickly merges into one of the sequences obtained using a value from {a(n)} as b(1):
  b(1) =  3 -> {3, 6, 25, 281, 961, ...},    which quickly merges into A090566
    (as does the result of using b(1) = 6 or 12 or 20 ...);
  b(1) =  5 -> {5, 29, 241, 1809, ...},      which quickly merges into A265147
    (as does the result of using b(1) = 7 ...);
  b(1) =  9 -> {9, 61, 504, 4516, ...},      which quickly merges into A265148;
  b(1) = 13 -> {13, 69, 169, 744, 769, ...}, which quickly merges into A265151.

Mathematica

See the Mmca coding in A090566 or A265147-A265154.

Crossrefs

Cf. A090566, A243091, A265147, A265148, A265149, A265150, A265151, A265152, A265153, A265154.

Sequence in context: A028836 A028838 A178332 * A070305 A174567 A178330

Adjacent sequences: A265152 A265153 A265154 * A265156 A265157 A265158

Keyword

nonn,base,more

Author

Robert G. Wilson v, Dec 02 2015

Status

approved