1,2

It is understood that a(n) is taken to be the smallest number >= a(n-1) which is compatible with the description.

Also called Silverman's sequence.

Vardi gives several identities satisfied by A001463 and this sequence.

We can interpret A001462 as a triangle: start with 1; 2,2; 3,3; and proceed by letting the row sum of row m-1 be the number of elements of row m. The partial sums of the row sums give 1, 5, 11, 38, 272, ... Conjecture: this proceeds as Lionel Levile's sequence A014644. See also A113676. - Floor van Lamoen, fvlamoen(AT)hotmail.com, Nov 06 2005.

The g.f. -z*(-1+z**4+z**7-z**8+z**9-z**3-z-z**11+z**12)/(1+z)/(z**2+1)/(z-1)**2 conjectured by S. Plouffe in his 1992 dissertationd is wrong. - njas, May 13 2008

G. Everest, A. van der Poorten, I. Shparlinski and T. Ward, Recurrence Sequences, Amer. Math. Soc., 2003; p. 10.

S. W. Golomb, Problem 5407, Amer. Math. Monthly, 73 (1966), 674.

R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 1990, p. 66.

J. Grytczuk, Another variation on Conway's recursive sequence, Discr. Math. 282 (2004), 149-161.

R. K. Guy, Unsolved Problems in Number Theory, E25.

D. Marcus and N. J. Fine, Solutions to Problem 5407, Amer. Math. Monthly 74 (1967), 740-743.

Petermann, Y.-F. S., On Golomb's self-describing sequence, J. Number Theory 53 (1995), 13-24.

Petermann, Y.-F. S., On Golomb's self-describing sequence, II, Arch. Math. (Basel) 67 (1996), 473-477.

Petermann, Y.-F. S., Is the error term wild enough? Analysis (Munich) 18 (1998), 245-256.

Petermann, Y.-F. S. and Remy, Jean-Luc, Golomb's self-described sequence and functional-differential equations, Illinois J. Math. 42 (1998), 420-440.

J. L. Remy, J. Number Theory, 66 (1997), 1-28.

J. Sauerberg and L. Shu, The long and the short on counting sequences, Amer. Math. Monthly, 104 (1997), 306-317.

I. Vardi, The error term in Golomb's sequence, J. Number Theory, 40 (1992), 1-11. (See also the Math. Review, 93d:11103)

T. D. Noe, Table of n, a(n) for n = 1..10000

B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, J. Integer Seqs., Vol. 6 (2003), #03.2.2.

B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence (math.NT/0305308)

Y.-F. S. Petermann, J.-L. Remy and I. Vardi, Discrete derivatives of sequences, Adv. in Appl. Math. 27 (2001), 562-84.

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures}, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

N. J. A. Sloane, My favorite integer sequences, in Sequences and their Applications (Proceedings of SETA '98).

N. J. A. Sloane, Seven Staggering Sequences.

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Index entries for "core" sequences

Index entries for sequences of the a(a(n)) = 2n family

a(n) = phi^(2-phi)*n^(phi-1) + E(n), where phi is the golden number (1+sqrt(5))/2 (Marcus and Fine) and E(n) is an error term which Vardi shows is O( n^(phi-1) / log n ).

a(1) = 1; a(n+1) = 1 + a(n+1-a(a(n))). - C. L. Mallows.

a(1)=1, a(2)=2 and for a(1)+a(2)+..+a(n-1) < k <= a(1)+a(2)+...+a(n) we have a(k)=n - Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 07 2003

G.f.: Sum_{k>0} x^a(k). - Michael Somos Oct 21 2006

a(1) = 1, so 1 only appears once. The next term is therefore 2, which means 2 appears twice, and so a(3) is also 2 but a(4) must be 3. And so on.

t1 := [ 1, 2, 2 ]: for i from 3 to 20 do t2 := t1; for j from 1 to t1[ i ] do t2 := [ op(t2), i ]; od: t1 := t2; od: t1; A001462 := n->t1[n];

a[1] = 1; a[n_] := a[n] = 1 + a[n - a[a[n - 1]]]; Table[ a[n], {n, 84}] (from Robert G. Wilson v (rgwv(at)rgwv.com), Aug 26 2005)

(PARI) a=[ 1, 2, 2 ]; for(n=3, 20, for(i=1, a[ n ], a=concat(a, n))); a

(PARI) {a(n)=local(A, t, i); if(n<3, max(0, n), A=vector(n); t=A[i=2]=2; for(k=3, n, A[k]=A[k-1]+if(t--==0, t=A[i++ ]; 1)); A[n])} /* Michael Somos Oct 21 2006 */

(MAGMA) [ n eq 1 select 1 else 1+Self(n-Self(Self(n-1))) : n in [1..100] ]; - from Sergei Haller (sergei(AT)sergei-haller.de), Dec 21 2006

Cf. A000002, A001463 (partial sums).

Sequence in context: A126848 A067085 A055086 this_sequence A082462 A005041 A030530

Adjacent sequences: A001459 A001460 A001461 this_sequence A001463 A001464 A001465

easy,nonn,nice,core

njas