A130870 Palindromic primes with squareful neighbors.

151, 727, 919, 10601, 14741, 15451, 15551, 16361, 16561, 19891, 30403, 31013, 33533, 34543, 35153, 39293, 70507, 71317, 72227, 73637, 75557, 78787, 79397, 93139, 94049, 94349, 94649, 94849, 94949, 95959, 97579, 1022201, 1055501

Offset

1,1

Comments

Sequence is the intersection of A075432 and A002385. - Chai Wah Wu, Jun 09 2015

Except for 11, every palindrome with an even number of digits is composite because divisible by 11; also, 11 that is the only palindromic prime with an even number of digits does not belong to this sequence because 10 is squarefree, hence all the terms of this sequence have an odd number of digits. - Bernard Schott, Feb 27 2020

Links

Chai Wah Wu, Table of n, a(n) for n = 1..1446

G. L. Honaker, Jr. and Chris K. Caldwell, Prime Curios! 151

Mathematica

squarefulQ[n_] := Last[Sort[Transpose[FactorInteger[n]][[2]]]] > 1; palindromeQ[n_] := Reverse[IntegerDigits[n]] == IntegerDigits[n]; Select[Range[3, 2000000], palindromeQ[ # ] && squarefulQ[ # - 1] && squarefulQ[ # + 1] && PrimeQ[ # ] &]
Select[Prime[Range[90000]], PalindromeQ[#]&&NoneTrue[#+{1, -1}, SquareFreeQ]&] (* Harvey P. Dale, Jul 19 2024 *)

Prog

(Python)
from sympy import isprime, factorint
def palgen10odd(l): # generator of palindromes in base 10 of odd length <= 2*l
    if l > 0:
        yield 0
        for x in range(1, l+1):
            for y in range(10**(x-1), 10**x):
                s = str(y)
                yield int(s+s[-2::-1])
A130870_list = []
for i in palgen10odd(5):
    if i > 2 and isprime(i) and max(factorint(i-1).values()) > 1 and max(factorint(i+1).values()) > 1:
        A130870_list.append(i) # Chai Wah Wu, Jun 09 2015
(PARI) isok(p) = isprime(p) && (p==fromdigits(Vecrev(digits(p)))) && !issquarefree(p-1) && !issquarefree(p+1); \\ Michel Marcus, Feb 27 2020

Crossrefs

Cf. A075432, A013929, A075432.

Sequence in context: A176138 A139640 A334836 * A340436 A211555 A143012

Adjacent sequences: A130867 A130868 A130869 * A130871 A130872 A130873

Keyword

base,nonn

Author

Tanya Khovanova, Jul 24 2007

Status

approved