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A376128 The absolute difference of two successive terms is prime and the absolute difference of two successive digits is also prime.

%I A376128 #16 Sep 12 2024 07:48:54
%S A376128 0,2,4,1,3,5,7,9,6,8,13,16,14,25,20,27,24,29,42,47,49,46,35,30,53,50,
%T A376128 31,36,38,57,52,41,64,61,63,58,69,72,70,75,86,81,68,135,74,79,242,469,
%U A376128 246,83,85,252,425,202,413,130,203,136,131,358,147,94,92,97,270,241,302,429,250,207,205,258,149
%N A376128 The absolute difference of two successive terms is prime and the absolute difference of two successive digits is also prime.
%H A376128 Michael S. Branicky, <a href="/A376128/b376128.txt">Table of n, a(n) for n = 1..10000</a>
%H A376128 Eric Angelini, <a href="https://cinquantesignes.blogspot.com/2024/09/more-digits-terms-and-primes.html">More digits, terms and primes</a>, personal blog of the author.
%e A376128 Terms a(1) to a(15) are 0,2,4,1,3,5,7,9,6,8,13,16,14,25,20.
%e A376128 The successive absolute differences between two terms are the primes 2,2,3,2,2,2,2,3,2,5,3,2,11,5.
%e A376128 The successive absolute differences between two digits are the primes 2,2,3,2,2,2,2,3,2,7,2,2,5,5,3,2,3,3,2.
%o A376128 (Python) # uses A219248gen in A219248
%o A376128 from sympy import isprime
%o A376128 from itertools import count, islice
%o A376128 def c(an, k):
%o A376128     return isprime(abs(an-k)) and isprime(abs(an%10-int(str(k)[0])))
%o A376128 def agen(): # generator of terms
%o A376128     an, aset = 0, {0}
%o A376128     while True:
%o A376128         yield an
%o A376128         an = next(k for k in A219248gen(seed=str(an%10)) if k not in aset and c(an, k))
%o A376128         aset.add(an)
%o A376128 print(list(islice(agen(), 73))) # _Michael S. Branicky_, Sep 11 2024
%Y A376128 Cf. A219248, A281878.
%K A376128 base,nonn
%O A376128 1,2
%A A376128 _Eric Angelini_ and _Jean-Marc Falcoz_, Sep 11 2024