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A244247
First prime in set of 3 palindromic primes in arithmetic progression ordered by the largest term in the progression.
1
3, 3, 11, 727, 10501, 13931, 10601, 10301, 14341, 16061, 12821, 12721, 10501, 12421, 15551, 13931, 13331, 30103, 30703, 30103, 30803, 31513, 31013, 74747, 70607, 73637, 72227, 70607, 73037, 79397, 94049, 93739, 90709, 95959, 96469, 94849
OFFSET
1,1
COMMENTS
This sequence is a subsequence of A002385, the palindromic primes.
The list is ordered based on the highest member of the arithmetic progression.
Some primes generate multiple progressions for different common differences.
REFERENCES
Albert H. Beiler, Recreations in the Theory of Numbers, Second Edition, Dower Publications Inc, page 222.
LINKS
The Prime Glossary, Palindromic Primes
EXAMPLE
a(1) = p = 3. For d = 2; [p , p+d, p+2d ] = [3, 5, 7] are in arithmetic progression and are palindromic.
a(2) = p = 3. For d = 4; [p , p+d, p+2d ] = [3, 7, 11] are in arithmetic progression and are palindromic.
a(5) = p = 10501. For d = 1920; [p , p+d, p+2d ] = [10501, 12421, 14341] are in arithmetic progression and are palindromic.
a(13) = p = 10501. For d = 3840; [p , p+d, p+2d ] = [10501, 14341, 18181] are in arithmetic progression and are palindromic.
[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
PROG
(PARI) ispal(n) = eval(concat(Vecrev(Str(n)))) == n;
ispp(p) = isprime(p) && ispal(p);
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
CROSSREFS
Cf. A002385 (palindromic primes).
Cf. A120627 (Least positive k such that both prime(n)+k and prime(n)+2k are prime, or 0 if no such k exists).
Sequence in context: A352857 A352582 A078225 * A211346 A163372 A349922
KEYWORD
nonn,base
AUTHOR
Abhiram R Devesh, Jun 23 2014
STATUS
approved