A270391 "Story primes" (see comments).

2, 3, 5, 7, 13, 29, 31, 41, 47, 53, 61, 79, 83, 97, 103, 163, 347, 367, 401, 487, 503, 521, 523, 541, 547, 563, 569, 587, 601, 709, 743, 769, 821, 823, 907, 941, 947, 967, 1063, 1069, 1481, 1609, 1621, 1663, 1669, 1847, 2887, 3607, 3863, 4001, 4889, 5003, 5021, 5023, 5081, 5281, 5441

Offset

1,1

Comments

A "story prime" is a prime on top of a descending triangle (such as the ones below) where every "story" is prime:

.

6 0 1 1 0 6 3 9 6 2 9

6 1 1 6 3 3 4 7

5 5 3 1 3

2 2

.

Each digit "d" must be the absolute difference of the two digits above "d". No leading zeros are accepted at any stage. The biggest such prime is 528888881, with 9 stories. There are only 128 such primes.

Links

Jean-Marc Falcoz, Table of n, a(n) for n = 1..128

Example

We see that the first 3 of the second row (from top) is the absolute difference between 5 and 2; the next digit is 6, the absolute difference between 2 and 8; etc.
  5 2 8 8 8 8 8 8 1
   3 6 0 0 0 0 0 7
    3 6 0 0 0 0 7
     3 6 0 0 0 7
      3 6 0 0 7
       3 6 0 7
        3 6 7
         3 1
          2

Mathematica

Select[Prime@ Range@ 720, Function[k, AllTrue[Most@ NestWhileList[Abs@ Differences@ # &, IntegerDigits@ k, # != {} &], And[First@ # != 0 &@ #, PrimeQ@ FromDigits@ #] &]]] (* Michael De Vlieger, Mar 16 2016, Version 10 *)

Crossrefs

Sequence in context: A158281 A115261 A063792 * A172508 A272107 A227880

Adjacent sequences: A270388 A270389 A270390 * A270392 A270393 A270394

Keyword

nonn,base,fini,full

Author

Eric Angelini and Jean-Marc Falcoz, Mar 16 2016

Status

approved