A115922 Numbers k such that k and 2*k, taken together are pandigital.

13485, 13548, 13845, 14538, 14685, 14835, 14853, 14865, 15486, 16485, 18546, 18645, 20679, 20769, 20793, 23079, 26709, 26907, 27069, 27093, 27309, 29067, 29073, 29307, 30729, 30792, 30927, 31485, 32079, 32709, 32907, 34851, 35148, 35481, 38145, 38451

Offset: 1

Author

Giovanni Resta, Feb 06 2006

Keywords

• nonn
• base
• fini
• full

Comments

Sequence contains 48 terms, the largest being 48651.

If leading zeros are permitted, there are 12 additional terms: 6729, 6792, 6927, 7269, 7293, 7329, 7692, 7923, 7932, 9267, 9273, 9327. - Harvey P. Dale, Feb 09 2014

Examples

			13485 and 26970=13485*2 together contain all the 10 digits once.
		

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..48 (full sequence)

Crossrefs

Cf. A050278, A054383, A115923, A115924, A115925, A114126, A115927.

Programs

Maple

for n from 12345 to 49382 do d:=[op(convert(n,base,10)), op(convert(2*n,base,10))]: pandig:=true: for k from 0 to 9 do if(numboccur(k,d)<>1)then pandig:=false: break: fi: od: if(pandig)then print(n): fi: od: # Nathaniel Johnston, May 31 2011

Mathematica

onehalfQ[n_]:=FromDigits[Take[n,5]]/FromDigits[Take[n,-5]]==1/2; FromDigits[ Take[#,5]]&/@Select[Permutations[Range[0,9]],onehalfQ] (* This program generates the full 60-term sequence, with leading zeros permitted, of which this sequence is a subset -- see Comments *) (* Harvey P. Dale, Feb 09 2014 *)

PARI

{for(n=10234,49876,#Set(digits(n))==5||next; #Set(digits(n*2))==5 && #Set(concat(digits(n),digits(n*2)))==10 && print1(n","))} \\ M. F. Hasler, Feb 08 2014