A052092 Lengths of the palindromic primes from Honaker's sequence A053600.

1, 3, 5, 9, 11, 15, 19, 23, 25, 31, 35, 41, 45, 49, 55, 59, 63, 69, 75, 81, 87, 93, 99, 105, 109, 113, 119, 125, 129, 133, 139, 145, 151, 157, 161, 167, 173, 179, 185, 191, 195, 201, 207, 213, 219, 225, 231, 237, 243, 249, 255, 261, 267, 273, 279, 285, 291, 297

Offset: 0

Author

Patrick De Geest, Jan 15 2000

Keywords

• nonn
• base

Comments

Since the terms from a(34) onward are currently only probable primes, the lengths given in this sequence beyond that point are only provisional.

For n > 0, a(n) = a(n-1)+2*m where m is the number of digits of A052091(n). - Chai Wah Wu, Dec 03 2015

Links

• Chai Wah Wu, Table of n, a(n) for n = 0..501

Crossrefs

Cf. A052091, A053600, A047076.

Programs

Python

from sympy import isprime
A052092_list, l, p = [1], 1, 2
for _ in range(100):
    m, ps = 1, str(p)
    s = int('1'+ps+'1')
    while not isprime(s):
        m += 1
        ms = str(m)
        if ms[0] in '268':
            ms = str(int(ms[0])+1) + '0'*(len(ms)-1)
            m = int(ms)
        if ms[0] in '45':
            ms = '7' + '0'*(len(ms)-1)
            m = int(ms)
        s = int(ms+ps+ms[::-1])
    p = s
    l += 2*len(ms)
    A052092_list.append(l) # Chai Wah Wu, Dec 02 2015

Extensions

Comments from G. L. Honaker, Jr., Mar 30 2000

Edited by T. D. Noe, Oct 30 2008