Constant sequences

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Constant sequences are sequences for which all terms are the same. Formally, sequences $\scriptstyle \{a(n)\}_{n=i_{\text{min}}}^{i_{\text{max}}}$ such that

$a(n+1)=a(n),\quad i_{\rm {min}}\leq n<i_{\rm {max}}.$

The all 1's sequence (A000012) is an example of a constant sequence. Others include A000004, A007395, A010692, A010701, A010709, A010716, A010722, A010727, A010731, A010734, A010850, A010851, A010852, A010853, A010854, A010855, A010856, A010857, A010858, A010859, A010860, A010861, A010862, A010863, A010864, A010865, A010866, A010867, A010868, A010869, A010870, and A010871.

In a sequence with members drawn from any partially ordered set, constant sequences are precisely those which are both nondecreasing and nonincreasing. (In fact, this holds in any preordered set.)

Eventually constant sequences

A generalization of constant sequences allows a finite prefix of arbitrary terms.

Constant sequences, as well as eventually constant sequences, are linear recurrences with signature (1).