Problems & Puzzles: Puzzles

Puzzle 728. Consecutive Moran numbers (extending the OEIS sequence A235397)

A number n is a Moran number if n divided by the sum of its decimal digits is prime.

The OEIS sequence A235397 shows the first term of the least sequence of n consecutive Moran numbers a(n), for n=1, 2,... , 6

18, 152, 3031, 21481224, 25502420, 4007565001480

a(6) = 4007565001480 because

4007565001480 = 40 * 100189125037,

4007565001481 = 41 * 97745487841,

4007565001482 = 42 * 95418214321,

4007565001483 = 43 * 93199186081,

4007565001484 = 44 * 91081022761,

4007565001485 = 45 * 89057000033

and

4007565001486 = 2*36191*55366873 <>46*prime

 

 

Q. Can you find some few next terms in this sequence?


Contributions came from J. K. Andersen

***

Andersen wrote:

Possible values from an inexhaustive search:
a(7): 2196125475223740
a(8): 905295493763807066010

...

A search using the second-largest known prime shows that
58402851*(2^43112609-1) and 58403625*(2^43112609-1) are 12978197-digit Moran numbers. The larger 2^57885161-1 did not produce similar solutions.

***

 

Records   |  Conjectures  |  Problems  |  Puzzles