A244247 - OEIS

%I #41 Apr 03 2023 10:36:13

%S 3,3,11,727,10501,13931,10601,10301,14341,16061,12821,12721,10501,

%T 12421,15551,13931,13331,30103,30703,30103,30803,31513,31013,74747,

%U 70607,73637,72227,70607,73037,79397,94049,93739,90709,95959,96469,94849

%N First prime in set of 3 palindromic primes in arithmetic progression ordered by the largest term in the progression.

%C This sequence is a subsequence of A002385, the palindromic primes.

%C The list is ordered based on the highest member of the arithmetic progression.

%C Some primes generate multiple progressions for different common differences.

%D Albert H. Beiler, Recreations in the Theory of Numbers, Second Edition, Dower Publications Inc, page 222.

%H Abhiram R Devesh, <a href="/A244247/b244247.txt">Table of n, a(n) for n = 1..1015</a>

%H The Prime Glossary, <a href="https://t5k.org/glossary/xpage/PalindromicPrime.html">Palindromic Primes</a>

%e a(1) = p = 3. For d = 2; [p , p+d, p+2d ] = [3, 5, 7] are in arithmetic progression and are palindromic.

%e a(2) = p = 3. For d = 4; [p , p+d, p+2d ] = [3, 7, 11] are in arithmetic progression and are palindromic.

%e a(5) = p = 10501. For d = 1920; [p , p+d, p+2d ] = [10501, 12421, 14341] are in arithmetic progression and are palindromic.

%e a(13) = p = 10501. For d = 3840; [p , p+d, p+2d ] = [10501, 14341, 18181] are in arithmetic progression and are palindromic.

%e [3, 7, 11] is an instance with d>p. With first term 110909011, there are 4 instances of common difference d greater than p, yielding 3 palindromic primes in arithmetic progression: d=9914652990, 9916572990, 9925563990, 9928383990. - _Michel Marcus_, Jul 21 2014

%o (PARI) ispal(n) = eval(concat(Vecrev(Str(n)))) == n;

%o ispp(p) = isprime(p) && ispal(p);

%o isokppap(p) = {if (ispp(p), for (d=1, p-1, if (ispp(p-d) && ispp(p-2*d), return (1));); return (0););} \\ _Michel Marcus_, Jul 07 2014

%Y Cf. A002385 (palindromic primes).

%Y Cf. A120627 (Least positive k such that both prime(n)+k and prime(n)+2k are prime, or 0 if no such k exists).

%K nonn,base

%O 1,1

%A _Abhiram R Devesh_, Jun 23 2014