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),
...
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.
CROSSREFS
KEYWORD
nonn,base,more
AUTHOR
Robert G. Wilson v, Dec 02 2015
STATUS
approved