|
%I #26 Jul 28 2015 04:30:01
%S 12,13,320,3201,72200,89000,132110,345000,643000,2320200,3121300,
%T 10103111,11300130,42430000,51340000,64030000,72300000,86300000,
%U 125102000,130213000,211220001,220101111,323111000,431130000,614110000,667000000,2153100000,2521002000,3021211100
%N Numbers n = d_0d_1...d_n (n < 10) such that d_i is the number of digits equal to i in n (base b), where b is less than 10.
%C The only terms having the same number of digits as the base are 13, 10103111, 211220001 and 220101111. For example, 13 is 1101_2, which has 1 zero and 3 ones.
%C The least term with 10 digits that describes itself is 2153100000.
%C 2153100000 is 104233022322_7, so it has 2 zeros, 1 one, 5 twos, 3 threes, 1 four, 0 fives, 0 sixes, 0 sevens, 0 eights and 0 nines in base 7.
%e 12 = 110_3, which has 1 zero and 2 ones.
%e 13 = 1101_2, which has 1 zero and 3 ones.
%e 320 = 11000_4, which has 3 zeros, 2 ones and 0 twos.
%e 3201 = 100301_5, which has 3 zeros, 2 ones, 0 twos and 1 three.
%e 72200 = 10200001002_3
%e 89000 = 10101101110101000_2
%e 132110 = 13211420_5
%e 345000 = 122112020210_3
%e 643000 1012200000211_3
%e 42430000 = 2201312320300_4
%e 51340000 = 3003312023200_4
%e 64030000 = 3310100110300_4
%e 72300000 = 122002100000_5
%e 86300000 = 20000101111100022_3
%e 431130000 = 110440340120_6
%e 614110000 = 2224203010000_5
%e 667000000 = 1201111002002222201_3
%e 2153100000 = 104233022322_7
%Y Cf. A001155, A001387, A005150, A046043, A138480.
%K nonn,base,fini,full
%O 1,1
%A _Pieter Post_, Jul 24 2015
%E a(10)-a(13), a(19)-a(23), a(28)-a(29) added by _Giovanni Resta_, Jul 26 2015
|
