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A156322 Integers n such that if you insert between each of their digits either "*" (times), "^" (exponentiation), or "nothing" (so that two or more digits are merged to form an integer), then you can recover n in a nontrivial way (however, two "^" mustn't be adjacent - you must avoid decompositions containing a^b^c). 2
2592, 34425, 35721, 312325, 344250, 357210, 492205, 1492992, 1729665, 1769472, 3123250, 3365793, 3442500, 3472875, 3572100, 3639168, 4922050, 6718464, 6967296, 7587328, 10744475, 10756480, 13745725, 13942125, 14569245, 16746975, 17266392, 17296650, 17577728, 17694720 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The number of terms in the sequence is infinite, because there are numbers like 34425 = 3^4*425, 344250 = 3^4*4250, 3442500 = 3^4*42500, etc.

LINKS

Table of n, a(n) for n=1..30.

Jean-Marc Falcoz, Illustration

EXAMPLE

      2592 = 2^5 * 9^2

     34425 = 3^4 * 425

     35721 = 3^5 * 7 * 21

    312325 = 31^2 * 325

    344250 = 3^4 * 4250

    357210 = 3^5 * 7 * 210

    492205 = 49^2 * 205

   1492992 = 1 * 4 * 9 * 2^9 * 9^2

   1729665 = 17^2 * 9 * 665

   1769472 = 1^7 * 6 * 9 * 4^7 * 2

   3123250 = 31^2 * 3250

   3365793 = 3*3^6 * 57 * 9 * 3

   3442500 = 3^4 * 42500

   3472875 = 3^4 * 7^2 * 875

   3572100 = 3^5 * 7 * 2100

   3639168 = 3^6 * 39 * 16 * 8

   4922050 = 49^2 * 2050

   6718464 = 6^7 * 1^84 * 6 * 4

   6967296 = 6 * 9 * 6 * 7 * 2^9 * 6

   7587328 = 7 * 58 * 73 * 2^8

  10744475 = 1^0 * 7^4 * 4475

  10756480 = 10 * 7^5 * 64 * 8^0

  13745725 = 1^3 * 7^4 * 5725

  13942125 = 1^3 * 9^4 * 2125

  14569245 = 1^4 * 569^2 * 45

  16746975 = 1^6 * 7^4 * 6975

  17266392 = 172 * 66 * 39^2

  17296650 = 17^2 * 9 * 6650

  17577728 = 17 * 577 * 7 * 2^8

  17694720 = 1^7 * 6 * 9 * 4^7 * 20.

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

3^5 * 1482 * 9760 = 3514829760

is the only pandigital with this property. - Jean-Marc Falcoz, Mar 19 2009

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

17 * 577 * 7 * 2^8 = 17577728

1297 * 7^3 * 31 * 941 = 12977331941

are the only composite integers up to 10^11 that are printer's errors with decomposition in prime factors. - Jean-Marc Falcoz, Sep 09 2018

CROSSREFS

Two other versions of the "printer's errors" sequence are A096298 and A116890.

This one is harder to compute because it's more general; you can have decompositions like ab*c*def^g*h*ij.

Sequence in context: A035894 A179702 A258728 * A096298 A204782 A204775

Adjacent sequences:  A156319 A156320 A156321 * A156323 A156324 A156325

KEYWORD

base,nonn

AUTHOR

Jean-Marc Falcoz, Feb 08 2009, Feb 14 2009

EXTENSIONS

Edited by N. J. A. Sloane, Feb 22 2009

STATUS

approved

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Last modified November 18 01:20 EST 2018. Contains 317279 sequences. (Running on oeis4.)