A343677 - OEIS

%I #23 Sep 03 2021 20:36:37

%S 4,6,19,34,100,241,697,1779,6590,16585,57237,179291,591325,1707010,

%T 6520756,18271423,65212230,210339179,706823539

%N Number of (2n+1)-digit undulating alternating palindromic primes.

%C a(n) is the number of (2n+1)-digit terms in A343675.

%C a(n) <= A057332(n).

%o (Python)

%o from sympy import isprime

%o def f(w):

%o     for s in w:

%o         for t in range(int(s[-1])+1,10,2):

%o             yield s+str(t)

%o def g(w):

%o     for s in w:

%o         for t in range(1-int(s[-1])%2,int(s[-1]),2):

%o             yield s+str(t)

%o def A343677(n):

%o     if n == 0:

%o         return 4

%o     c = 0

%o     for d in '1379':

%o         x = d

%o         for i in range(1,n+1):

%o             x = g(x) if i % 2 else f(x)

%o         c += sum(1 for p in x if isprime(int(p+p[-2::-1])))

%o         y = d

%o         for i in range(1,n+1):

%o             y = f(y) if i % 2 else g(y)

%o         c += sum(1 for p in y if isprime(int(p+p[-2::-1])))

%o     return c

%Y Cf. A002385, A030144, A057332, A059168, A343590.

%K nonn,base,more

%O 0,1

%A _Chai Wah Wu_, Apr 25 2021

%E a(17)-a(18) from _Chai Wah Wu_, May 02 2021