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 A271527 a(n) = 1000^n + 1. 1
 2, 1001, 1000001, 1000000001, 1000000000001, 1000000000000001, 1000000000000000001, 1000000000000000000001, 1000000000000000000000001, 1000000000000000000000000001, 1000000000000000000000000000001, 1000000000000000000000000000000001 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS All terms in this sequence are palindromes (A002113). Also, A062395 written in base 2 (see example). a(n) minus one gives the number of nodes at n-th level of a 1000-ary tree. More generally, the ordinary generating function for sequences of the form k^n + m, is (1 + m - (1 + k*m)*x)/((1 - x)*(1 - k*x)), and the exponential generating function is exp(k*x) + m*exp(x). LINKS Index entries for linear recurrences with constant coefficients, signature (1001,-1000) FORMULA G.f.: (2 - 1001*x)/((1 - x)*(1 - 1000*x)). E.g.f.: exp(1000*x) + exp(x). a(n) = 1001*a(n-1) - 1000*a(n-2). a(n) = A060365(n) + 1. a(n) = A000533(3n), n>0. a(n) = A007088(A062395(n)). A007953(a(n)) = A007395(n). A000035(a(n)) = A057427(n). Sum_{n>=0} 1/a(n) = 0.501000001999002... Lim_{n->infinity} a(n + 1)/a(n) = 1000. EXAMPLE a(n), n>0, is the binary representation of A062395(n) n  ------------------------------------------ 0  2........................................2 1  1001.....................................9 2  1000001.................................65 3  1000000001.............................513 4  1000000000001.........................4097 5  1000000000000001.....................32769 6  1000000000000000001.................262145 7  1000000000000000000001.............2097153 8  1000000000000000000000001.........16777217 9  1000000000000000000000000001.....134217729 MATHEMATICA Table[1000^n + 1, {n, 0, 11}] LinearRecurrence[{1001, -1000}, {2, 1001}, 12] PROG (PARI) x='x+O('x^99); Vec((2-1001*x)/((1-x)*(1-1000*x))) \\ Altug Alkan, Apr 09 2016 (Python) for n in xrange(0, 10**4):print(1000**n+1) # Soumil Mandal, Apr 10 2016 CROSSREFS Cf. A000035, A000533, A007088, A007395, A007953, A057427, A060365, A062395, A152756. Sequence in context: A079233 A194191 A190579 * A214543 A258661 A024033 Adjacent sequences:  A271524 A271525 A271526 * A271528 A271529 A271530 KEYWORD nonn,base,easy AUTHOR Ilya Gutkovskiy, Apr 09 2016 STATUS approved

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Last modified January 23 11:04 EST 2019. Contains 319391 sequences. (Running on oeis4.)