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A296450

Integers N that yield exactly 10 different digits when all products of two successive digits of N are considered.

1633956, 1633965, 1659336, 1659933, 1693365, 1775428, 1775442, 1778425, 1783365, 1853394, 1853397, 1923956, 1923965, 1932956, 1932965, 1936690, 1936940, 1936970, 1942593, 1942598, 1952493, 1952498, 1963940, 1963970, 1966390, 1986532, 2335689, 2336593, 2336598, 2339563, 2339956, 2339965

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

nDigits Count Min Max

------- ----- ---------- ----------

6 0

7 286 1633956 9985197

8 1254 11561774 99851332

9 1708 113245177 985113324

10 468 1123315817 9185132117

11 0

There are no 6-digit or 11-digit integers that produce the digits 0 to 9 by multiplication of two contiguous digits of N. The smallest such integer is 1633956; the largest one is 9185132117; the sequence has 3716 terms.

LINKS

Lars Blomberg, Table of n, a(n) for n = 1..3716

EXAMPLE

The first term is 1633956. The successive products of two contiguous digits of 1633956 are 1*6=6, 6*3=18, 3*3=9, 3*9=27, 9*5=45, 5*6=30. We see that 6, 18, 9, 27, 45 and 30 include all digits 0 to 9, none being repeated.

MATHEMATICA

Select[Range[163*10^4, 234*10^4], Sort[Flatten[IntegerDigits/@ (Times@@@ Partition[ IntegerDigits[ #], 2, 1])]]==Range[0, 9]&] (* Harvey P. Dale, Dec 17 2020 *)

CROSSREFS

Sequence in context: A173428 A015334 A015377 * A255042 A255035 A256953

Adjacent sequences: A296447 A296448 A296449 * A296451 A296452 A296453

KEYWORD

nonn,base,fini

AUTHOR

Eric Angelini and Lars Blomberg, Dec 13 2017

STATUS

approved