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A270391 "Story primes" (see comments). 1
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 (list; graph; refs; listen; history; text; internal format)
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 (don't consider the dots):

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

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Last modified September 24 06:13 EDT 2021. Contains 347623 sequences. (Running on oeis4.)