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A343675
Undulating alternating palindromic primes.
3
2, 3, 5, 7, 101, 181, 383, 727, 787, 929, 10301, 10501, 14341, 16361, 16561, 18181, 30103, 30703, 32323, 36563, 38183, 38783, 70507, 72727, 74747, 78787, 90709, 94949, 96769, 1074701, 1092901, 1212121, 1218121, 1412141, 1616161, 1658561, 1856581, 1878781, 3072703
OFFSET
1,1
COMMENTS
All terms have an odd number of decimal digits.
For n > 3, a(n) is odd and not divisible by 5.
Intersection of A002385, A030144 and A059168.
Subsequence of A343590.
EXAMPLE
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.
MATHEMATICA
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 *)
PROG
(Python)
from sympy import isprime
def f(w):
for s in w:
for t in range(int(s[-1])+1, 10, 2):
yield s+str(t)
def g(w):
for s in w:
for t in range(1-int(s[-1])%2, int(s[-1]), 2):
yield s+str(t)
A343675_list = [2, 3, 5, 7]
for l in range(1, 9):
for d in '1379':
x = d
for i in range(1, l+1):
x = g(x) if i % 2 else f(x)
A343675_list.extend([int(p+p[-2::-1]) for p in x if isprime(int(p+p[-2::-1]))])
y = d
for i in range(1, l+1):
y = f(y) if i % 2 else g(y)
A343675_list.extend([int(p+p[-2::-1]) for p in y if isprime(int(p+p[-2::-1]))])
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Chai Wah Wu, Apr 25 2021
STATUS
approved