|
| |
|
|
A001477
|
|
The nonnegative integers.
|
|
315
| |
|
|
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77
(list; table; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
COMMENTS
| Although this is a list, and lists normally have offset 1, it seems better to make an exception in this case. - N. J. A. Sloane, Mar 13 2010
The subsequence 0,1,2,3,4 gives the known values of n such that 2^(2^n)+1 is a prime (see A019434, the Fermat primes). - N. J. A. Sloane, Jun 16 2010.
Contribution from Eric Desbiaux (moongerms(AT)wanadoo.fr), Nov 15 2009: It appears that, with the Bachet-Bezout theorem, A001477 = (2*A080425) + (3*A008611) and A000040 = (2*A039701)+(3*A157966).
a(n) = A007966(n)*A007967(n). [Reinhard Zumkeller, Jun 18 2011]
Besides the first term, this sequence is the denominator in the Maclaurin series of ln 2, which is 1 - 1/2 + 1/3 - 1/4 +.... - Mohammad K. Azarian, Oct 15 2011
|
|
|
REFERENCES
| Paul Barry, A Catalan Transform and Related Transformations on Integer Sequences, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.5.
|
|
|
LINKS
| N. J. A. Sloane, Table of n, a(n) for n = 0..500000
Index entries for "core" sequences
Index entries for sequences that are permutations of the natural numbers
Index entries for sequences related to linear recurrences with constant coefficients
Tanya Khovanova, Recursive Sequences
Eric Weisstein's World of Mathematics, Natural Number
Eric Weisstein's World of Mathematics, Nonnegative Integer
Robert G. Wilson v, American English names for the numbers from 0 to 100999 without spaces or hyphens.
|
|
|
FORMULA
| a(n)=n; a(0) = 0, a(n) = a(n-1)+1; G.f.: x/(1-x)^2.
Multiplicative with a(p^e) = p^e. - David W. Wilson (davidwwilson(AT)comcast.net), Aug 01, 2001.
When seen as array: T(k, n) = n + (k+n)*(k+n+1)/2. Main diagonal is 2n(n+1) (A046092), antidiagonal sums are n(n+1)(n+2)/2 (A027480). - Ralf Stephan, Oct 17 2004
Dirichlet generating function: zeta(s-1). - Franklin T. Adams-Watters, Sep 11 2005.
E.g.f. x*e^x. - Franklin T. Adams-Watters, Sep 11 2005.
a(0)=0, a(1)=1, a(n)=2*a(n-1)-a(n-2). - Jaume Oliver i Lafont (joliverlafont(AT)gmail.com), May 07 2008
Contribution from Eric Desbiaux (moongerms(AT)wanadoo.fr), Oct 28 2008: Alternating partial sums give A001057 = A000217 - 2*(A008794)
A001477=(2*A028242)+(3*A059841) and A000040=(2*A067076)+3 [From Eric Desbiaux (moongerms(AT)wanadoo.fr), Dec 10 2009]
a(n)=Sum_k>=0 {A030308(n,k)*2^k}. - From DELEHAM Philippe, Oct 20 2011.
|
|
|
MAPLE
| [ seq(n, n=0..100) ];
|
|
|
MATHEMATICA
| Table[n, {n, 0, 100}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 08 2006
|
|
|
PROG
| (MAGMA) [ n : n in [0..100]];
(PARI) A001477(n)=n /* first term is a(0) */
|
|
|
CROSSREFS
| Cf. A000027 (n>=1).
Partial sums of A057427. - Jeremy Gardiner (jeremy.gardiner(AT)btinternet.com), Sep 08 2002
Sequence in context: A131738 A000027 * A087156 A033619 A130734 A090108
Adjacent sequences: A001474 A001475 A001476 * A001478 A001479 A001480
|
|
|
KEYWORD
| core,nonn,easy,mult,tabl
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
| |
|
|
