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A165411
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Primes p such that each of p's digits d appears consecutively exactly d times and p contains each nonzero digit up to its maximum digit.
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1
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223331, 122555554444333, 224444333555551, 224444555553331, 225555544441333, 333555554444221, 555552233344441, 555552244441333, 555554444221333, 122444455555666666333, 122555554444666666333, 144446666662255555333
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| This sequence is a subsequence of A140057, A078348, and A108571. There are 129 terms; the largest is 7777777666666444455555223331. As 1, 122, and 221 are not prime and any such numbers whose maximum digit is 4, 8, or 9 are divisible by 3, all terms of the sequence have either 6 (1 term), 15 (8 terms), 21 (24 terms), or 28 (96 terms) decimal digits (=triangular numbers A000217(n) for n=3,5,6,7, respectively).
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LINKS
| Rick L. Shepherd, Table of n, a(n) for n = 1..129.
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EXAMPLE
| 1333444455555226666667777777 is a term because it is a prime meeting the criteria: It contains all digits 1 through 7, its maximum, each appearing in a single run of length equal to the value of the digit.
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CROSSREFS
| Cf. A140057, A078348, A108571.
Sequence in context: A046396 A083640 A180949 * A204743 A048427 A203922
Adjacent sequences: A165408 A165409 A165410 * A165412 A165413 A165414
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KEYWORD
| base,easy,fini,nonn
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AUTHOR
| Rick L. Shepherd (rshepherd2(AT)hotmail.com), Sep 17 2009
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