A343675 Undulating alternating palindromic primes.

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.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

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

Cf. A002385, A030144, A059168, A343590.

Sequence in context: A092908 A050784 A030150 * A029977 A052019 A205529

Adjacent sequences: A343672 A343673 A343674 * A343676 A343677 A343678

Keyword

nonn,base

Author

Chai Wah Wu, Apr 25 2021

Status

approved