A321367 Palindromic primes p such that the highest factor of p+1 is a palindromic prime and the highest factor of p-1 is also a palindromic prime.

3, 5, 7, 11, 383, 38783, 12211811221, 18345254381, 36729292763, 70381018307, 1852347432581, 1874989894781, 115582393285511, 164257606752461, 187610727016781, 199239838932991, 374147565741473, 396089252980693, 15243433533434251, 18741272727214781, 32547212721274523

Offset

1,1

Links

Table of n, a(n) for n=1..21.

Example

383 is in the sequence because the highest factor of 383+1 is 3, which is a palindromic prime and the highest factor of 383-1 is 191, which is a palindromic prime.

Mathematica

Select[Prime@ Range[10^4], AllTrue[{FactorInteger[# - 1][[-1, 1]], #, FactorInteger[# + 1][[-1, 1]]}, And[PrimeQ@ #, PalindromeQ@ #] &] &] (* Michael De Vlieger, Nov 13 2018 *)

Prog

(PARI) forprime(n=3, 10^9, if(Vecrev(digits(n))==digits(n), s=factor(n-1); t=factor(n+1); s=component(s, 1); t=component(t, 1); s=s[length(s)]; t=t[length(t)]; if(Vecrev(digits(s))==digits(s), if(Vecrev(digits(t))==digits(t), print1(n, " , ")))))

Crossrefs

Cf. A002113, A002385.

Sequence in context: A069804 A245722 A262962 * A121976 A339789 A293598

Adjacent sequences: A321364 A321365 A321366 * A321368 A321369 A321370

Keyword

nonn,base

Author

Paolo Galliani, Nov 07 2018

Extensions

a(11)-a(21) from Giovanni Resta, Nov 08 2018

Status

approved