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A219248 Numbers such that the absolute difference of any two adjacent (decimal) digits is prime.

%I A219248 #25 Dec 23 2024 14:53:43
%S A219248 0,1,2,3,4,5,6,7,8,9,13,14,16,18,20,24,25,27,29,30,31,35,36,38,41,42,
%T A219248 46,47,49,50,52,53,57,58,61,63,64,68,69,70,72,74,75,79,81,83,85,86,92,
%U A219248 94,96,97,130,131,135,136,138,141,142,146,147,149,161,163,164
%N A219248 Numbers such that the absolute difference of any two adjacent (decimal) digits is prime.
%C A219248 Numbers which may (and do) occur in A219250 and A219249 (union {0}).
%C A219248 This is to A219250 and A219249 what A182175 is to A182177 and A182178.
%H A219248 Michael S. Branicky, <a href="/A219248/b219248.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harvey P. Dale)
%H A219248 E. Angelini, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2013-April/011035.html">Any digit-pair in S sums to a prime</a>, SeqFan list, Apr 11 2013
%t A219248 Select[Range[0,200],And@@PrimeQ[Abs[Differences[IntegerDigits[#]]]]&] (* _Harvey P. Dale_, Jun 06 2014 *)
%o A219248 (PARI) is_A219248(n)={!for(i=2,#n=digits(n),isprime(abs(n[i-1]-n[i]))||return)}
%o A219248 (Python)
%o A219248 def ok(n):
%o A219248     d = list(map(int, str(n)))
%o A219248     return all(abs(d[i]-d[i-1]) in {2,3,5,7} for i in range(1, len(d)))
%o A219248 print([k for k in range(164) if ok(k)]) # _Michael S. Branicky_, Sep 11 2024
%o A219248 (Python)
%o A219248 from itertools import count, islice
%o A219248 def A219248gen(seed=None): # generator of terms
%o A219248     nxt = {None:"123456789", "0":"2357", "1":"3468", "2":"04579",
%o A219248         "3":"01568", "4":"12679", "5":"02378", "6":"13489",
%o A219248         "7":"02459", "8":"1356", "9":"2467"}
%o A219248     def bgen(d, seed=None):
%o A219248         if d == 0: yield tuple(); return
%o A219248         yield from ((i,)+t for i in nxt[seed] for t in bgen(d-1, seed=i))
%o A219248     yield 0
%o A219248     for d in count(1):
%o A219248         yield from (int("".join(t)) for t in bgen(d, seed=seed))
%o A219248 print(list(islice(A219248gen(), 65))) # _Michael S. Branicky_, Sep 11 2024
%K A219248 nonn,base
%O A219248 1,3
%A A219248 _M. F. Hasler_, Apr 12 2013