A320969 Semiprimes with distinct digits.

4, 6, 9, 10, 14, 15, 21, 25, 26, 34, 35, 38, 39, 46, 49, 51, 57, 58, 62, 65, 69, 74, 82, 85, 86, 87, 91, 93, 94, 95, 106, 123, 129, 134, 142, 143, 145, 146, 158, 159, 169, 178, 183, 185, 187, 194, 201, 203, 205, 206, 209, 213, 214, 215, 217, 218, 219, 235, 237, 247, 249, 253, 254, 259, 265, 267, 274

Offset: 1

Author

Zak Seidov, Oct 25 2018

Keywords

• nonn
• base
• fini

Comments

This sequence has 864939 terms, the last being 987654301.

Number of n-digit terms, for n = 1..9: 3, 27, 183, 1140, 6240, 27666, 99543, 277146, 452991. There are no semiprimes with distinct digits for n > 9.

Indeed, a 10-digit pandigital number is divisible by 9=3*3, so it can't be semiprime, and there are not more than 10 distinct digits in base 10. - M. F. Hasler, Oct 29 2018

Examples

			a(n*10^5) for n= 1..8: 6710843 = 173*38791, 30541627 = 881*34667, 62148035 = 5*12429607, 95068217 = 41*2318737, 280196547 = 3*93398849, 476891503 = 11*43353773, 654037129 = 79*8278951, 861247059 = 3*287082353.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Intersection of A001358 and A010784.

Cf. A029743.

Programs

Mathematica

Select[Range[300],PrimeOmega[#]==2&&Max[DigitCount[#]]==1&] (* Harvey P. Dale, Jan 29 2022 *)

PARI

is(n)=bigomega(n)==2&& #Set(n=digits(n))=#n \\ M. F. Hasler, Oct 29 2018

PARI

row(n,L=List())=forvec(d=vector(n,i,[0,9]),for(i=!d[1]*(n-1)!,n!-1,bigomega(fromdigits(vecextract(d,numtoperm(n,i))))==2||next;  listput(L,fromdigits(vecextract(d,numtoperm(n,i))))),2);Set(L) \\ Returns the n-digit terms. - M. F. Hasler, Oct 29 2018

Extensions

More terms from M. F. Hasler, Oct 29 2018