

A007395


Constant sequence: the all 2's sequence.
(Formerly M0208)


76



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
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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(n1,1).  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+j2)^2.  Michel Marcus, Dec 23 2015
For p = prime(n+2), a(n) = ord_p(H_(p1)), where ord_p denotes the padic valuation and H_i = 1 + 1/2 + ... + 1/i is a harmonic sum, except for n = 1944 and n = 157504, where ord_p(H_(p1)) = 3, and any other term of A088164 that may exist (see Conrad link). The sequence a(n) = ord_p(H_(p1)) does not have its own entry in the OEIS.  Felix Fröhlich, Mar 16 2016


REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

Table of n, a(n) for n=1..102.
K. Conrad, The padic 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 to divisibility sequences
Index entries for recurrences a(n) = k*a(n  1) +/ a(n  2)
Index entries for linear recurrences with constant coefficients, signature (1).


FORMULA

G.f.: 2/(1x), and e.g.f.: 2*e^x.  Mohammad K. Azarian, Dec 22 2008


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, A010701, A089105.
Cf. A213999, A254858.
Sequence in context: A084100 A130130 A046698 * A036453 A040000 A239374
Adjacent sequences: A007392 A007393 A007394 * A007396 A007397 A007398


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane.


STATUS

approved



