A085775 Numbers k such that (k / sum of digits of k) and (k+1 / sum of digits of k+1) are both prime.

152, 803, 1016, 1853, 3031, 3032, 3438, 7361, 7542, 7587, 8226, 8337, 10095, 10278, 10307, 11354, 11646, 13116, 13117, 13881, 17153, 21434, 21906, 23412, 26221, 28824, 30254, 31112, 32166, 34218, 35513, 38322, 40335, 41058, 44373, 45380

Offset

1,1

Comments

The sequence lists the first of two such consecutive numbers. There are very few instances of three such consecutive numbers -- in the first 100,000 numbers, only 3031, 13116, and 46824 are the first of three such consecutive numbers. And there are no instances of four such consecutive numbers in the first 10 million numbers. - Harvey P. Dale, Jul 08 2026

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

152 is a term since 152/(1+5+2) = 19 and 153/(1+5+3) = 17 are both prime.

Mathematica

moranQ[n_] := PrimeQ[n / Plus @@ IntegerDigits[n]]; Select[Range[50000], moranQ[#] && moranQ[#+1] &] (* Amiram Eldar, Apr 25 2020 *)
SequencePosition[Table[If[PrimeQ[n/Total[IntegerDigits[n]]], 1, 0], {n, 46000}], {1, 1}][[;; , 1]] (* Harvey P. Dale, Jul 08 2026 *)

Crossrefs

Subsequence of A001101 and A330927.

Sequence in context: A259740 A253359 A226365 * A208492 A208485 A364815

Adjacent sequences: A085772 A085773 A085774 * A085776 A085777 A085778

Keyword

base,nonn

Author

Jason Earls, Jul 23 2003

Extensions

Offset corrected by Amiram Eldar, Apr 25 2020

Status

approved