cp's OEIS Frontend

A350570 a(n) is the smallest multiple of 7 that can be formed by concatenating the first n positive integers in some order.

%I A350570 #20 Feb 15 2022 16:35:19
%S A350570 21,231,3241,12453,123564,1234576,12347685,123456879,10123456798,
%T A350570 1011123456798,101111223456789,10111121323457896,1011112131423457896,
%U A350570 101111213141523456879,10111121314151623456789,1011112131415161723456789,101111213141516171823458796
%N A350570 a(n) is the smallest multiple of 7 that can be formed by concatenating the first n positive integers in some order.
%e A350570 (2, 1)   21
%e A350570 (2, 3, 1)   231
%e A350570 (3, 2, 4, 1)   3241
%e A350570 (1, 2, 4, 5, 3)   12453
%e A350570 (1, 2, 3, 5, 6, 4)   123564
%e A350570 (1, 2, 3, 4, 5, 7, 6)   1234576
%e A350570 (1, 2, 3, 4, 7, 6, 8, 5)   12347685
%e A350570 (1, 2, 3, 4, 5, 6, 8, 7, 9)   123456879
%e A350570 From _Jon E. Schoenfield_, Jan 07 2022: (Start)
%e A350570 Observation: for each term from a(2) through a(18), if the positive integers are originally arranged in a string of digits in order from 1 through 9 (or 1 through n for n < 9), left to right, and then (for n > 9) the remaining numbers are incorporated into the string by placing '10' to the left of the initial '1' and then placing all remaining numbers in order from left to right between the '1' and the '2' (e.g., so as to yield the concatenation 10/1/11/12/13/14/15/16/17/18/2/3/4/5/6/7/8/9 for n=18), then at most 4 digits at the right end of the concatenated string need to be rearranged to obtain a(n), as shown here, where a space is inserted to the left of the digits (if any) that need to be rearranged:
%e A350570                             21
%e A350570                            231
%e A350570                           3241
%e A350570                         12 453
%e A350570                        123 564
%e A350570                       12345 76
%e A350570                      1234 7685
%e A350570                     123456 879
%e A350570                   101234567 98
%e A350570                 10111234567 98
%e A350570               101111223456789
%e A350570             1011112132345 7896
%e A350570           101111213142345 7896
%e A350570         101111213141523456 879
%e A350570       10111121314151623456789
%e A350570     1011112131415161723456789
%e A350570   10111121314151617182345 8796
%e A350570 (End)
%Y A350570 Cf. A008589.
%K A350570 nonn,base
%O A350570 2,1
%A A350570 _Claudio Meller_, Jan 06 2022
%E A350570 a(12)-a(18) from _Jon E. Schoenfield_, Jan 06 2022