

A154634


Numbers that are the first of two consecutive primes having a sum that is the product of two consecutive numbers.


3



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
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OFFSET

1,1


COMMENTS

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.


LINKS

Klaus Brockhaus, Table of n, a(n) for n=1..1000 [From Klaus Brockhaus, Jan 15 2009]


FORMULA

{A000040(i): A001043(i) in A002378}.  R. J. Mathar, Jan 15 2009


EXAMPLE

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.  Klaus Brockhaus, Jan 15 2009


MAPLE

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: # R. J. Mathar, 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); # Emeric Deutsch, Jan 15 2009


PROG

(MAGMA) [ p: p in PrimesUpTo(18000)  r*(r+1) eq s where r is Iroot(s, 2) where s is p+NextPrime(p) ]; // Klaus Brockhaus, Jan 15 2009


CROSSREFS

Sequence in context: A082093 A045455 A160031 * A232655 A175866 A227500
Adjacent sequences: A154631 A154632 A154633 * A154635 A154636 A154637


KEYWORD

easy,nonn


AUTHOR

J. M. Bergot, Jan 13 2009


EXTENSIONS

Corrected and extended by several correspondents, Jan 15 2009


STATUS

approved



