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Search: id:A089180
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| A089180 |
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a(n) is the smallest number m such that d(m) = d(m+1) = ... = d(m+n), where d(k) = prime(k+1)-prime(k) (A001223). |
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1
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OFFSET
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1,1
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COMMENT
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a(5) is greater than 105000000.
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REFERENCES
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L. J. Lander and T. R. Parkin, Consecutive primes in arithmetic progression, Math. Comp. vol 21 no 99 (1967) p 489.
G. W. Polites, Prime Desert n-Tuplets, Amer. Math. Monthly vol 95 no 2 (1988) p 98-104.
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LINKS
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J. K. Andersen, The minimal CPAP-k.
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FORMULA
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A000040[a(n)]=A006560(n+2). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 10 2007
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EXAMPLE
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a(3) = 659426 because d(659426) = d(659426+1) = d(659426+2) = d(6594286+3) or 9843019, 9843049, 9843079, 9843109, 9843139 are five consecutive primes with same difference and prime(659426) = 9843019 is the smallest prime number with this property.
Also a(4) = 6904737 because d(6904737) = d(6904737+1) = ... = d(6904737+4) or 121174811, 121174841, 121174871, 121174901, 121174931, 121174961 are six consecutive primes with same difference and prime(6904737) = 121174811 is the smallest prime number with this property.
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CROSSREFS
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Cf. A001223, A090403.
Sequence in context: A122418 A069788 A117681 this_sequence A034013 A157262 A007975
Adjacent sequences: A089177 A089178 A089179 this_sequence A089181 A089182 A089183
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KEYWORD
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more,nonn
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AUTHOR
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Farideh Firoozbakht (f.firoozbakht(AT)sci.ui.ac.ir), Dec 07 2003
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