A080723 a(0) = 1; 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".

1, 4, 5, 6, 7, 10, 13, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 28, 31, 34, 37, 40, 43, 46, 49, 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, 78, 79, 82, 85, 88, 91, 94, 97, 100, 103, 106, 109, 112, 115, 118, 121, 124

Offset

0,2

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..67.

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) {print1(1, ", "); a=4; m=[4]; for(n=2, 68, print1(a, ", "); a=a+1; 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: A039024 A065028 A107756 * A288737 A139448 A356398

Adjacent sequences: A080720 A080721 A080722 * A080724 A080725 A080726

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