A281592 Products of three distinct primes p1, p2 and p3 (sphenic numbers) with p1<p2 and p3 is the concatenation of p1 with p2.

138, 777, 4642, 10258, 10263, 12207, 13282, 16167, 19762, 30783, 37407, 38482, 46978, 48927, 56127, 60145, 63543, 73767, 81687, 89823, 95367, 95627, 103863, 110905, 115527, 128545, 202705, 208879, 223643, 284119, 324947, 325793, 360151, 395003, 477538, 541163, 558322, 585538, 672199, 673693, 780082, 914551, 1016643

Offset

1,1

Links

Table of n, a(n) for n=1..43.

Example

10258 is in the sequence because 10258 = 2*23*223 and 223 is the concatenation of 2 with 23.

Mathematica

c[x_, y_] := x 10^IntegerLength[y] + y; upto[mx_] := Sort@ Reap[Block[{p=2, q=3, v=1}, While[v <= mx, While[p < q && (v = p q (r = c[p, q])) <= mx, If[PrimeQ@r, Sow@v]; p = NextPrime[p]]; p=2; q = NextPrime[q]; v = p q c[p, q]]]][[2, 1]]; upto[10^6] (* Giovanni Resta, Apr 14 2017 *)

Prog

(PARI) isok(n) = f = factor(n); ((#f~ == 3) && (vecmax(f[, 2]) == 1) && (f[3, 1] == fromdigits(concat(digits(f[1, 1]), digits(f[2, 1]))))); \\ Michel Marcus, Apr 14 2017

Crossrefs

Cf. A007304, A133980 (the p3 primes).

Sequence in context: A168531 A260133 A317579 * A213963 A279964 A163693

Adjacent sequences: A281589 A281590 A281591 * A281593 A281594 A281595

Keyword

nonn,base

Author

Peter Weiss, Apr 14 2017

Status

approved