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Search: id:A157772
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| A157772 |
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Numbers a(n) such that 100*a(n)+13 is prime. |
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+0
6
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| 0, 1, 3, 6, 10, 12, 16, 19, 21, 22, 27, 33, 34, 36, 40, 45, 48, 51, 54, 58, 61, 70, 72, 85, 87, 90, 94, 96, 103, 105, 106, 111, 112, 118, 121, 124, 126, 127, 133, 135, 136, 139, 147, 148, 150, 153, 154, 159, 177, 180, 183, 184, 187, 189, 190, 192, 198, 199, 201, 210, 213, 216
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OFFSET
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1,3
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COMMENT
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1) The sequence is infinite, because by Dirichlet's theorem there are infinitely many primes in the arithmetic sequence A*n+B (n=1,2,...) if A an B are relatively prime.
2) The sequence has also an infinite set of pairs a(k+1)=a(k)+1 (two consecutive naturals), but no set of three consecutive naturals (each third natural is divisible by 3)
3) No term of the sequence is of form 3k+2, because the sum of digits of 100*(3k+2)+13 is divisible by 3, violating the requirement of the definition.
4) indices (as k-th prime) of the first members are: 6, 30, 65, 112, 170, 198, 255, 293, 319, 330, 396, 466, 480, 505, 554, 612, 648, 684, 714, 763, 797, 902, 922, 1061, 1086, 1121, 1164, 1186, 1265, 1286, 1295,...
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FORMULA
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{a(n): 100*a(n)+13 in A000040}.
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EXAMPLE
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a(1)=0: 100*0+13=13 smallest prime which ends on 13, see A000040(6). a(2)=1: 100*1+13=113 second prime which ends on 13, see A000040(30).
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CROSSREFS
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Cf. A088262 (6th row) - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 18 2009
Sequence in context: A114981 A007960 A032732 this_sequence A082925 A131696 A164114
Adjacent sequences: A157769 A157770 A157771 this_sequence A157773 A157774 A157775
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KEYWORD
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nonn
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AUTHOR
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Ulrich Krug (leuchtfeuer37(AT)gmx.de), Mar 06 2009
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EXTENSIONS
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Edited, inserted 27 - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 18 2009
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