A135355 Semiprimes with digits in ascending order.

4, 6, 9, 14, 15, 25, 26, 34, 35, 38, 39, 46, 49, 57, 58, 69, 123, 129, 134, 145, 146, 158, 159, 169, 178, 235, 237, 247, 249, 259, 267, 278, 289, 346, 358, 458, 469, 478, 489, 579, 589, 679, 689, 789, 1234, 1238, 1247, 1257, 1267, 1345, 1346, 1347, 1349, 1357

Offset: 1

Author

Jonathan Vos Post, Dec 08 2007

Keywords

• nonn
• base
• easy
• fini
• full

Comments

This is to A028864 as A001358 is to A000040. Semiprime metadromes in base 10. Contains 175 terms, the last being a(175)=12345789 = 3 * 4115263.

Snapshots: a(100)=13579, a(150)=135689, a(160)=245678, a(163)=356789, a(169)=1346789, a(173)=2356789. - R. J. Mathar, Dec 11 2007

Links

• R. J. Mathar, Table of n, a(n) for n = 1..175

Crossrefs

Cf. A001358, A028864.

Programs

Maple

isA001358 := proc(n) if numtheory[bigomega](n) = 2 then true; else false ; fi ; end: isA009993 := proc(n) local dgs,i ; dgs := convert(n,base,10) ; if nops(dgs) = 1 then RETURN(true) ; fi ; for i from 1 to nops(dgs)-1 do if op(i,dgs) <= op(i+1,dgs) then RETURN(false) ; fi ; od: RETURN(true) ; end: isA135355 := proc(n) isA001358(n) and isA009993(n) ; end: for n from 4 to 1400 do if isA135355(n) then printf("%d, ",n) ; fi ; od: # R. J. Mathar, Dec 11 2007
# second Maple program:
b:= proc(n) n, seq(b(10*n+j), j=irem(n, 10)+1..9) end:
select(numtheory[bigomega]=2, {seq(b(n), n=1..9)})[];  # Alois P. Heinz, Apr 13 2025

Mathematica

Select[Range[1357],PrimeOmega[#]==2&&AllTrue[Differences[IntegerDigits[#]],Positive]&] (* James C. McMahon, Apr 13 2025 *)

Formula

Equals A001358 INTERSECT A009993. - R. J. Mathar, Dec 11 2007

Extensions

Corrected by R. J. Mathar, Dec 11 2007