A308252 - OEIS

%I #20 May 20 2019 10:49:51

%S 46,58,93,111,143,187,209,265,295,403,422,446,454,458,466,478,481,482,

%T 497,502,511,514,526,538,542,553,554,562,566,586,713,851,921,933,939,

%U 951,993,1011,1041,1047,1059,1077,1101,1111,1119,1133,1137,1149,1167,1177,1191,1199

%N Squarefree composite numbers k with chained prime factors: the last digit of every prime factor is the same as the first digit of the next one. Prime factors must be in ascending order.

%C This sequence contains all squarefree numbers of A308099.

%e 1426 is such a number because it is a squarefree composite, with prime factors in ascending order 2, 23 and 31 which are chained.

%t Select[Range@1500,SquareFreeQ@#&&PrimeNu@#>1&&And@@(Last@#[[1]]==First@#[[2]]&/@Partition[IntegerDigits@*First/@FactorInteger@#,2,1])&]

%o (PARI) isok(n) = {my(f=factor(n)[, 1]); if ((#f <= 1) || !issquarefree(n), return(0)); my(vd=digits(f[1]), d=vd[#vd], vd2, d2); if ((#f <= 1) || !issquarefree(n), return(0)); for (k=2, #f, vd2 = digits(f[k]); d2 = vd2[1]; if (d2 != d, return (0)); vd = vd2; d = vd[#vd];); return (1);} \\ _Michel Marcus_, May 18 2019

%Y Cf. A005117, A308099, A308101.

%K nonn,base

%O 1,1

%A _Giorgos Kalogeropoulos_, May 17 2019