1,1

N-th Early bird number A116700(n) is in the sequence if it occurs in the concatenation of the first n-1 early bird numbers, A116700(1), ..., A116700(n-1).

With A116700 as early bird numbers of order 1, this can be generalized to define early bird numbers of order k for k > 1: N-th Early bird number of order k-1 is an early bird number of order k if it occurs in the concatenation of the first n-1 early bird numbers of order k-1.

Inspired by Eric Angelini's posting to Seq Fan mailing list, Jul 23, 2007.

K. Brockhaus, Table of n, a(n) for n = 1..1000

A116700(45) = 99 occurs in the concatenation 1221233132344142434551525354566162636465677172737475767881828384858687899192939495969798 of A116700(1), ..., A116700(44). Hence 99 is an early bird number of order 2.

(JBASIC) Program works for order >= 1; set maxterm >= A133652(order).

order = 2

maxterm = 374 : dim seq(maxterm), early(maxterm)

for i = 1 to maxterm : seq(i) = i : next

for k = 1 to order

concatenation$ = "" : n = 0

for j = 1 to maxterm

term = seq(j) : string$ = str$(term)

if instr(concatenation$, string$) > 0 then n = n+1 : early(n) = term

concatenation$ = concatenation$ + string$

next j

maxterm = n : redim seq(maxterm)

for i = 1 to maxterm : seq(i) = early(i) : next

redim early(maxterm)

next k

print "early bird numbers of order "; order

for i = 1 to maxterm : print seq(i); ", "; : next

Cf. A116700 (early bird numbers), A133651 (early bird numbers of order 3), A133652 (least early bird number of order n).

Sequence in context: A033419 A110397 A072433 this_sequence A045298 A039446 A095420

Adjacent sequences: A133647 A133648 A133649 this_sequence A133651 A133652 A133653

nonn,base

Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Sep 19 2007