A306661 - OEIS

A306661

Numbers with chained divisors: Numbers k with divisors such that the last digit of every divisor is the same as the first digit of the next divisor.

%I #36 May 07 2019 11:31:18

%S 1,11,13,17,19,101,103,107,109,113,121,127,131,137,139,149,151,157,

%T 163,167,173,179,181,191,193,197,199,1009,1013,1019,1021,1031,1033,

%U 1039,1049,1051,1061,1063,1069,1087,1091,1093,1097,1103,1109,1111

%N Numbers with chained divisors: Numbers k with divisors such that the last digit of every divisor is the same as the first digit of the next divisor.

%C All prime numbers whose first digit is 1 (A045707) have this property.

%C The first composite numbers having this property are A307858: 121, 1111, 1207, ...

%e 14641 is such a number because its divisors are 1, 11, 121, 1331, 14641.

%e Also, 90043 is in the sequence because its divisors are 1, 127, 709, 90043 and the last digit of every divisor is the first digit of the next one.

%t Select[Range@1500,And@@(Last@#[[1]]==First@#[[2]]&/@Partition[IntegerDigits/@Divisors@#,2,1])&]

%Y A307858 and A045707 are subsequences.

%K nonn,base

%O 1,2

%A _Giorgos Kalogeropoulos_, May 05 2019