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A343675 Undulating alternating palindromic primes.

%I A343675 #18 Apr 26 2021 21:26:10
%S A343675 2,3,5,7,101,181,383,727,787,929,10301,10501,14341,16361,16561,18181,
%T A343675 30103,30703,32323,36563,38183,38783,70507,72727,74747,78787,90709,
%U A343675 94949,96769,1074701,1092901,1212121,1218121,1412141,1616161,1658561,1856581,1878781,3072703
%N A343675 Undulating alternating palindromic primes.
%C A343675 All terms have an odd number of decimal digits.
%C A343675 For n > 3, a(n) is odd and not divisible by 5.
%C A343675 Intersection of A002385, A030144 and A059168.
%C A343675 Subsequence of A343590.
%H A343675 Chai Wah Wu, <a href="/A343675/b343675.txt">Table of n, a(n) for n = 1..10000</a>
%e A343675 16361 is a term as it is a palindromic prime, the digits 1, 6, 3, 6 and 1 have odd and even parity alternately, and also alternately rise and fall.
%t A343675 Union@Flatten[{{2,3,5,7},Array[Select[FromDigits/@Riffle@@@Tuples[{Tuples[{1,3,5,7,9},#],Tuples[{0,2,4,6,8},#-1]}],(s=Union@Partition[Sign@Differences@IntegerDigits@#,2];(s=={{1,-1}}||s=={{-1,1}})&&PrimeQ@#&&PalindromeQ@#)&]&,4]}] (* _Giorgos Kalogeropoulos_, Apr 26 2021 *)
%o A343675 (Python)
%o A343675 from sympy import isprime
%o A343675 def f(w):
%o A343675     for s in w:
%o A343675         for t in range(int(s[-1])+1,10,2):
%o A343675             yield s+str(t)
%o A343675 def g(w):
%o A343675     for s in w:
%o A343675         for t in range(1-int(s[-1])%2,int(s[-1]),2):
%o A343675             yield s+str(t)
%o A343675 A343675_list = [2,3,5,7]
%o A343675 for l in range(1,9):
%o A343675     for d in '1379':
%o A343675         x = d
%o A343675         for i in range(1,l+1):
%o A343675             x = g(x) if i % 2 else f(x)
%o A343675         A343675_list.extend([int(p+p[-2::-1]) for p in x if isprime(int(p+p[-2::-1]))])
%o A343675         y = d
%o A343675         for i in range(1,l+1):
%o A343675             y = f(y) if i % 2 else g(y)
%o A343675         A343675_list.extend([int(p+p[-2::-1]) for p in y if isprime(int(p+p[-2::-1]))])
%Y A343675 Cf. A002385, A030144, A059168, A343590.
%K A343675 nonn,base
%O A343675 1,1
%A A343675 _Chai Wah Wu_, Apr 25 2021