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Search: id:A129918
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| A129918 |
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Smallest prime of the form k*prime(n+1)+prime(n)=j*prime(n+2)+prime(n+1) for free integer multipliers k and j. |
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1
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| 23, 103, 271, 271, 557, 3209, 2411, 6229, 2633, 401, 2251, 28163, 19219, 13297, 3121, 46663, 17749, 2339, 41389, 25037, 121259, 261031, 6491, 19489, 41507, 192917, 163171, 6211, 4177, 440549, 59863, 247279, 120233, 21893, 102829, 435041, 13523
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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A prime (like 271) ocurring more than once ought be rare. It requires four primes to be linked by two congruences. The sequence of the 2nd smallest primes of the form is 53, 173, 733, 557, 2767, 5147, 4159, 12899, 6229... The list of 3rd smallest primes is 83, 313, 887, 1129, 3209, 8377, 6781, 16901,... - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 02 2007
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EXAMPLE
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For n=3, prime(3,4,5)=(5,7,11), we have 38*7+5=24*11+7=271, a prime, with (k,j)=(38,24).
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MAPLE
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A129918 := proc(n) local p, q, r, m ; p := ithprime(n) ; q := nextprime(p) ; r := nextprime(q) ; m := chrem([p, q], [q, r]) ; while not isprime(m) do m := m+ r*q ; od ; RETURN(m) ; end: seq(A129918(n), n=1..40) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 02 2007
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CROSSREFS
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Somewhat related to A072999.
Adjacent sequences: A129915 A129916 A129917 this_sequence A129919 A129920 A129921
Sequence in context: A142173 A139976 A142192 this_sequence A138715 A096324 A044274
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KEYWORD
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nonn
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AUTHOR
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J. M. Bergot (thekingfishb(AT)yahoo.ca), Jun 05 2007
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EXTENSIONS
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Edited by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 02 2007
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