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Search: id:A154634
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| A154634 |
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The sequence list the first of two consecutive primes having a sum that is the product of two consecutive numbers. |
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1
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| 5, 13, 19, 43, 103, 113, 229, 293, 349, 463, 739, 773, 859, 1171, 1429, 1483, 3079, 3229, 3319, 3823, 4003, 4273, 5449, 6781, 6899, 7129, 7369, 7499, 7873, 7993, 10729, 11173, 11321, 11779, 12241, 12553, 13523, 13693, 14533, 14699, 17203, 17389
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Is the sequence mostly uniformly distributed or do clusters occur for the products? One could also find sums of 2n consecutive primes equaling the product of 2n numbers.
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LINKS
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Klaus Brockhaus, Table of n, a(n) for n=1..1000 [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 15 2009]
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FORMULA
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{A000040(i): A001043(i) in A002378}. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 15 2009]
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EXAMPLE
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For the pair of consecutive primes 1429 and 1433, their sum is 2862=53*54.
773 and 787 are consecutive primes. 773+787 = 1560 = 39*40, hence 773 is in the sequence. [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 15 2009]
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MAPLE
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isA002378 := proc(n) local a; a := floor(sqrt(n)) ; RETURN( a*(a+1) = n ) ; end: for i from 1 to 5000 do p := ithprime(i) ; a001043 := p+nextprime(p) ; if isA002378(a001043) then printf("%d, ", p) ; fi; od: [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 15 2009]
a := proc (n) local p, s: p := ithprime(n): s := p+nextprime(p): if type((1/2)*sqrt(1+4*s)-1/2, integer) = true then p else end if end proc: seq(a(n), n = 1 .. 3000); [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 15 2009]
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PROGRAM
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(MAGMA) [ p: p in PrimesUpTo(18000) | r*(r+1) eq s where r is Iroot(s, 2) where s is p+NextPrime(p) ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 15 2009]
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CROSSREFS
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Sequence in context: A082093 A045455 A160031 this_sequence A087714 A055045 A030374
Adjacent sequences: A154631 A154632 A154633 this_sequence A154635 A154636 A154637
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KEYWORD
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base,easy,nonn
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AUTHOR
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J. M. Bergot (thekingfishb(AT)yahoo.ca), Jan 13 2009
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EXTENSIONS
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Corrected and extended by several correspondents, Jan 15 2009
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