A235397 The first term of the least sequence of n consecutive Moran numbers.

18, 152, 3031, 21481224, 25502420, 4007565001480, 2196125475223740, 905295493763807066010

Offset: 1

Author

Carlos Rivera, Jan 09 2014

Keywords

• nonn
• hard
• base
• fini
• more

Comments

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

From Amiram Eldar, Apr 25 2020: (Start)

Jens Kruse Andersen found that a(7) <= 2196125475223740 and a(8) <= 905295493763807066010 (see Rivera link).

Since Moran numbers (A001101) are also Niven numbers (A005349), this sequence is finite with no more than 20 terms (see A060159). (End)

a(9) <= 270140199032572375590810. - Giovanni Resta, Apr 30 2020

Examples

			a(6) = 4007565001480 because
4007565001480 = 40 * 100189125037,
4007565001481 = 41 * 97745487841,
4007565001482 = 42 * 95418214321,
4007565001483 = 43 * 93199186081,
4007565001484 = 44 * 91081022761,
4007565001485 = 45 * 89057000033.
		

Links

• Giovanni Resta, Moran numbers
• Carlos Rivera, Puzzle 728. Consecutive Moran numbers, The Prime Puzzles & Problems Connection.

Crossrefs

Cf. A001101, A060159, A085775.

Programs

PARI

isA001101(n)=(k->denominator(k)==1&&isprime(k))(n/sumdigits(n))
a(n)=my(k=n); while(1, forstep(i=k,k-n+1,-1, if(!isA001101(i), k=i+n; next(2))); return(k-n+1)) \\ Charles R Greathouse IV, Jan 10 2014

Extensions

a(7)-a(8) from Giovanni Resta, Apr 27 2020