A080724 - OEIS

A080724

a(0) = 2; for n>0, a(n) is taken to be the smallest positive integer greater than a(n-1) which is consistent with the condition "n is a member of the sequence if and only if a(n) == 1 mod 3".

2, 3, 4, 7, 10, 11, 12, 13, 14, 15, 16, 19, 22, 25, 28, 31, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 55, 58, 61, 64, 67, 70, 73, 76, 79, 82, 85, 88, 91, 94, 97, 100, 103, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,1

REFERENCES

Hsien-Kuei Hwang, S Janson, TH Tsai, Exact and asymptotic solutions of the recurrence f(n) = f(floor(n/2)) + f(ceiling(n/2)) + g(n): theory and applications, Preprint, 2016; http://140.109.74.92/hk/wp-content/files/2016/12/aat-hhrr-1.pdf. Also Exact and Asymptotic Solutions of a Divide-and-Conquer Recurrence Dividing at Half: Theory and Applications, ACM Transactions on Algorithms, 13:4 (2017), #47; DOI: 10.1145/3127585

LINKS

Table of n, a(n) for n=0..65.

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)

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

FORMULA

a(a(n)) = 3*n+4, n >= 0.

PROG

(PARI) {a=2; m=[2]; for(n=1, 66, print1(a, ", "); a=a+1; if(a%3==1&&a==n, qwqw=qwqw, if(m==[], while(a%3!=1&&a==n, a++), if(m[1]==n, while(a%3!=1, a++); m=if(length(m) == 1, [], vecextract(m, "2..")), if(a%3==1, a++))); m=concat(m, a)))}

CROSSREFS

Cf. A079000, A080720, ...

Sequence in context: A182832 A375723 A082673 * A342780 A089589 A047546

Adjacent sequences: A080721 A080722 A080723 * A080725 A080726 A080727

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Mar 08 2003

EXTENSIONS

More terms and PARI code from Klaus Brockhaus, Mar 08 2003

STATUS

approved