A211186 Smallest strictly increasing sequence such that no term is the sum of any two digits of the sequence.

1, 2, 4, 7, 44, 47, 48, 49, 74, 77, 78, 79, 84, 87, 88, 89, 94, 97, 98, 99, 444, 447, 448, 449, 474, 477, 478, 479, 484, 487, 488, 489, 494, 497, 498, 499, 744, 747, 748, 749, 774, 777, 778, 779, 784, 787, 788, 789, 794, 797, 798, 799, 844, 847, 848, 849, 874, 877

Offset

1,2

Comments

"Smallest" means lexicographically (1 < 2 < 10 < ...) first.

From a(2)=2 on, there may not occur any other term with the digit 1. From a(3)=4 on, the digits 2 and 3 are excluded. From a(4)=7 on, the digits 5 and 6 are excluded. From a(5)=44 on, the digit 0 is also excluded, and subsequent terms are all larger numbers made from digits 4,7,8 or 9; one can check that then no further contradictions can appear.

Thus there are 4^d terms with d digits, for d=1,2,3,... This leads to an explicit formula for the n-th term.

Links

Table of n, a(n) for n=1..58.

E. Angelini, Post to the SeqFan mailing list, Feb 02 2013

Prog

(PARI) A211186(n)={n>4 & for(d=1, n--, n < 4^d & return(sum(k=1, d, [4, 7, 8, 9][n%4+1]*10^(k-1)+0*n\=4)); n -= 4^d); [1, 2, 4, 7][n]}

Crossrefs

Sequence in context: A082537 A004577 A285940 * A302938 A076719 A103009

Adjacent sequences: A211183 A211184 A211185 * A211187 A211188 A211189

Keyword

nonn,base

Author

Eric Angelini and M. F. Hasler, Feb 02 2013

Status

approved