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 A130621 List the first term of each triple of consecutive primes with the property that their sum is the square of a prime. 2
 13, 37, 277, 313, 613, 7591, 8209, 12157, 23053, 32233, 42953, 44887, 105649, 225769, 245941, 258707, 287671, 331333, 342049, 346111, 347443, 393853, 560719, 721267, 867253, 1001089, 1064431, 1219849, 1545127, 1556623, 1617727, 1752607 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Robert Israel, Table of n, a(n) for n = 1..3000 EXAMPLE (37, 41, 43) is a triple of consecutive prime numbers; their sum is 121 which is a prime squared. Hence 37 is in the sequence. MAPLE f:= proc(n) local p, q, r; q:= prevprime(floor(n/3)); p:= prevprime(q); r:= nextprime(q); if p+q+r = n then return p elif p+q+r < n then while p+q+r < n do p:= q; q:= r; r:= nextprime(r); od; if p+q+r = n then return p fi else while p+q+r > n do r:= q; q:= p; p:= prevprime(p); od; if p+q+r = n then return p fi; fi; false end proc: R:= NULL: count:= 0: p:= 3: while count < 100 do p:= nextprime(p); v:= f(p^2); if v::integer then R:= R, v; count:= count+1; fi od: R; # Robert Israel, Sep 18 2022 MATHEMATICA a={}; For[n=1, n<100000, n++, If[PrimeQ[Sqrt[Prime[n]+Prime[n+1]+Prime[n+2]]], AppendTo[a, Prime[n]]]]; a Select[Partition[Prime[Range[132000]], 3, 1], PrimeQ[Sqrt[Total[#]]]&][[All, 1]] (* Harvey P. Dale, Dec 12 2022 *) CROSSREFS Sequence in context: A266882 A078952 A206279 * A309594 A098265 A195540 Adjacent sequences: A130618 A130619 A130620 * A130622 A130623 A130624 KEYWORD nonn AUTHOR J. M. Bergot, Jun 18 2007 EXTENSIONS Edited and extended by Stefan Steinerberger, Jun 23 2007 STATUS approved

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Last modified August 8 06:45 EDT 2024. Contains 375020 sequences. (Running on oeis4.)