A343677 Number of (2n+1)-digit undulating alternating palindromic primes.

4, 6, 19, 34, 100, 241, 697, 1779, 6590, 16585, 57237, 179291, 591325, 1707010, 6520756, 18271423, 65212230, 210339179, 706823539

Offset: 0

Author

Chai Wah Wu, Apr 25 2021

Keywords

• nonn
• base
• more

Comments

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

a(n) <= A057332(n).

Crossrefs

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

Programs

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)
def A343677(n):
    if n == 0:
        return 4
    c = 0
    for d in '1379':
        x = d
        for i in range(1,n+1):
            x = g(x) if i % 2 else f(x)
        c += sum(1 for p in x if isprime(int(p+p[-2::-1])))
        y = d
        for i in range(1,n+1):
            y = f(y) if i % 2 else g(y)
        c += sum(1 for p in y if isprime(int(p+p[-2::-1])))
    return c

Extensions

a(17)-a(18) from Chai Wah Wu, May 02 2021