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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 25 16:17 EDT 2019. Contains 326324 sequences. (Running on oeis4.)