A308099 Numbers k with 2 or more chained distinct prime factors: the last digit of every prime factor is the same as the first digit of the next prime factor. Prime factors must be in ascending order.

46, 58, 92, 93, 111, 116, 143, 184, 187, 209, 232, 265, 279, 295, 333, 368, 403, 422, 446, 454, 458, 464, 466, 478, 481, 482, 497, 502, 511, 514, 526, 538, 542, 553, 554, 562, 566, 586, 713, 736, 837, 844, 851, 892, 908, 916, 921, 928, 932, 933, 939, 951, 956, 964, 993, 999

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

144026 is such a number because its distinct prime factors in ascending order are 2, 23, 31, 101 and the last digit of each prime factor is the same as the first digit of the next one.

Maple

filter:= proc(n) local F, i;
  F:= sort(convert(numtheory:-factorset(n), list));
  nops(F) >= 2 and andmap(i -> F[i] mod 10 = floor(F[i+1]/10^ilog10(F[i+1])), [$1..nops(F)-1])
end proc:
select(filter, [$1..1000]); # Robert Israel, Jun 21 2019

Mathematica

Select[Range@1000, 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, return(0)); my(vd=digits(f[1]), d=vd[#vd], vd2, d2); 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. A307858, A308252, A308101.

Sequence in context: A330243 A326646 A332952 * A308252 A322161 A039424

Adjacent sequences: A308096 A308097 A308098 * A308100 A308101 A308102

Keyword

nonn,base

Author

Giorgos Kalogeropoulos, May 12 2019

Status

approved