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 A007395 Constant sequence: the all 2's sequence. (Formerly M0208) 116
 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Continued fraction for 1 + sqrt(2). - Philippe Deléham, Nov 14 2006 a(n) = A213999(n,1). - Reinhard Zumkeller, Jul 03 2012 The least witness function W(k) is defined for odd composite numbers k. The sequence W(k) does not have its own entry in the OEIS because W(k) = 2 for all k with 9 <= k < 2047; then W(2047)=3. Cf. A089105. - N. J. A. Sloane, Sep 17 2014 a(n) = A254858(n-1,1). - Reinhard Zumkeller, Feb 09 2015 a(n) = number of permutations of length n+2 having exactly one ascent such that the first element the permutation is 2. - Ran Pan, Apr 20 2015 With alternating signs, this is the sequence of determinants of the 3 X 3 matrices m with m(i,j) = Fibonacci(n+i+j-2)^2. - Michel Marcus, Dec 23 2015 For p = prime(n+2), a(n) = ord_p(H_(p-1)), where ord_p denotes the p-adic valuation and H_i = 1 + 1/2 + ... + 1/i is a harmonic sum, except for n = 1944 and n = 157504, where ord_p(H_(p-1)) = 3, and any other term of A088164 that may exist (see Conrad link). The sequence a(n) = ord_p(H_(p-1)) does not have its own entry in the OEIS. - Felix Fröhlich, Mar 16 2016 This sequence is the only infinite bounded sequence of positive integers such that a(n) = (a(n-1) + a(n-2)) / gcd(a(n-1), a(n-2)) for all n >= 2. - Bernard Schott, Dec 28 2018 REFERENCES Titu Andreescu and Dorin Andrica, Number Theory, Birkhäuser, 2009, from 1999 Russian Mathematical Olympiad, p. 347. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS 25th All-Russian Mathematical Olympiad, Grade 10, Problem 2, p. 2, 1999. Tobias Boege, Thomas Kahle, Construction Methods for Gaussoids, arXiv:1902.11260 [math.CO], 2019. K. Conrad, The p-adic growth of harmonic sums Daniele A. Gewurz and Francesca Merola, Sequences realized as Parker vectors of oligomorphic permutation groups, J. Integer Seqs., Vol. 6, 2003. R. H. Hardin, Binary arrays with both rows and cols sorted, symmetries Tanya Khovanova, Recursive Sequences Aram Tangboonduangjit, Thotsaporn Thanatipanonda, Determinants Containing Powers of Generalized Fibonacci Numbers, arXiv:1512.07025 [math.CO], 2015. Eric Weisstein's World of Mathematics, Hamiltonian Cycle Index entries for linear recurrences with constant coefficients, signature (1). FORMULA G.f.: 2/(1-x), and e.g.f.: 2*e^x. - Mohammad K. Azarian, Dec 22 2008 a(n) = A000005(A000040(n)). - Omar E. Pol, Feb 28 2018 a(n) = A002061(n) - A165900(n). - Torlach Rush, Feb 21 2019 MATHEMATICA Table[2, {105}] PROG (PARI) a(n) = 2 \\ Charles R Greathouse IV, Apr 07 2012 (Haskell) a007395 = const 2 a007395_list = repeat 2  -- Reinhard Zumkeller, May 07 2012 (Maxima) makelist(2, n, 0, 30); /* Martin Ettl, Nov 09 2012 */ CROSSREFS Cf. A000004, A000012, A002061, A010701, A089105, A165900. Cf. A213999, A254858. Sequence in context: A329683 A130130 A046698 * A036453 A040000 A239374 Adjacent sequences:  A007392 A007393 A007394 * A007396 A007397 A007398 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified September 26 09:30 EDT 2022. Contains 356993 sequences. (Running on oeis4.)