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%I #18 Apr 26 2021 21:26:10
%S 2,3,5,7,101,181,383,727,787,929,10301,10501,14341,16361,16561,18181,
%T 30103,30703,32323,36563,38183,38783,70507,72727,74747,78787,90709,
%U 94949,96769,1074701,1092901,1212121,1218121,1412141,1616161,1658561,1856581,1878781,3072703
%N Undulating alternating palindromic primes.
%C All terms have an odd number of decimal digits.
%C For n > 3, a(n) is odd and not divisible by 5.
%C Intersection of A002385, A030144 and A059168.
%C Subsequence of A343590.
%H Chai Wah Wu, <a href="/A343675/b343675.txt">Table of n, a(n) for n = 1..10000</a>
%e 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 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 (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 A343675_list = [2,3,5,7]
%o for l in range(1,9):
%o for d in '1379':
%o x = d
%o for i in range(1,l+1):
%o x = g(x) if i % 2 else f(x)
%o A343675_list.extend([int(p+p[-2::-1]) for p in x if isprime(int(p+p[-2::-1]))])
%o y = d
%o for i in range(1,l+1):
%o y = f(y) if i % 2 else g(y)
%o A343675_list.extend([int(p+p[-2::-1]) for p in y if isprime(int(p+p[-2::-1]))])
%Y Cf. A002385, A030144, A059168, A343590.
%K nonn,base
%O 1,1
%A _Chai Wah Wu_, Apr 25 2021
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