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A244247
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First prime in set of 3 palindromic primes in arithmetic progression ordered by the largest term in the progression.
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1
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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
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OFFSET
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1,1
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COMMENTS
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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.
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REFERENCES
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Albert H. Beiler, Recreations in the Theory of Numbers, Second Edition, Dower Publications Inc, page 222.
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LINKS
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EXAMPLE
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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
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PROG
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(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
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CROSSREFS
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Cf. A120627 (Least positive k such that both prime(n)+k and prime(n)+2k are prime, or 0 if no such k exists).
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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