A308252 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.

46, 58, 93, 111, 143, 187, 209, 265, 295, 403, 422, 446, 454, 458, 466, 478, 481, 482, 497, 502, 511, 514, 526, 538, 542, 553, 554, 562, 566, 586, 713, 851, 921, 933, 939, 951, 993, 1011, 1041, 1047, 1059, 1077, 1101, 1111, 1119, 1133, 1137, 1149, 1167, 1177, 1191, 1199

Offset

1,1

Comments

This sequence contains all squarefree numbers of A308099.

Links

Table of n, a(n) for n=1..52.

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A005117, A308099, A308101.

Sequence in context: A326646 A332952 A308099 * A322161 A039424 A043247

Adjacent sequences: A308249 A308250 A308251 * A308253 A308254 A308255

Keyword

nonn,base

Author

Giorgos Kalogeropoulos, May 17 2019

Status

approved