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?

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Contributions came from J. K. Andersen

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Andersen wrote:

Possible values from an non-exhaustive search:
a(7): 2196125475223740
a(8): 905295493763807066010

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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.

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Giovanni Resta wrote on April 2020

I have verified that J. K. Andersen's bounds
2196125475223740 and 905295493763807066010
are indeed a(7) and a(8) and I also found  that a(9) <=  270140199032572375590810, that is, 270140199032572375590810 starts a run of 9 consecutive Moran numbers, but it may not be the smallest.

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