A244247 First prime in set of 3 palindromic primes in arithmetic progression ordered by the largest term in the progression.

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

Abhiram R Devesh, Table of n, a(n) for n = 1..1015

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

Adjacent sequences: A244244 A244245 A244246 * A244248 A244249 A244250

Keyword

nonn,base

Author

Abhiram R Devesh, Jun 23 2014

Status

approved