A321367 - OEIS

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

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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