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Search: id:A129990
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| A129990 |
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Primes p such that the smallest integer whose sum of digits is p is prime. |
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+0
1
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| 2, 3, 5, 7, 11, 17, 19, 23, 29, 31, 41, 43, 71, 79, 97, 173, 179, 257, 269, 311, 389, 691, 4957, 8423, 11801, 14621, 25621, 26951, 38993, 75743, 102031, 191671, 668869
(list; graph; listen)
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OFFSET
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1,1
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FORMULA
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Primes p such that (p mod 9 + 1) * 10^[p/9] - 1 is prime. Therefore the sequence consists of primes of the forms A002957(k)*9+1, A056703(k)*9+2, A056712(k)*9+4, A056716(k)*9+5, A056721(k)*9+7, A056725(k)*9+8. [From Max Alekseyev]
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EXAMPLE
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The smallest integer whose sum of digits is 17 is 89; 89 is prime, therefore 17 is in the sequence.
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MATHEMATICA
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Select[Prime[Range[1000]], PrimeQ[FromDigits[Join[{Mod[ #, 9]}, Table[9, {i, 1, Floor[ #/9]}]]]] &]
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CROSSREFS
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Cf. A051885.
Sequence in context: A108543 A042988 A167135 this_sequence A162566 A040085 A040049
Adjacent sequences: A129987 A129988 A129989 this_sequence A129991 A129992 A129993
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KEYWORD
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hard,more,nonn,new
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AUTHOR
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J. M. Bergot (thekingfishb(AT)yahoo.ca), Jun 14 2007
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EXTENSIONS
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Edited, corrected and extended by Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Jun 23 2007
Extended by D. S. McNeil (d.mcneil(AT)qmul.ac.uk), Mar 20 2009
Five more terms from Max Alekseyev (maxale(AT)gmail.com), Nov 09 2009
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