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A242383
Lesser of consecutive primes whose average is an oblong number.
3
5, 11, 29, 41, 53, 71, 239, 337, 419, 461, 503, 547, 599, 647, 863, 1051, 1187, 1481, 1721, 1801, 2549, 2647, 2969, 3539, 4421, 6317, 7129, 8009, 10301, 12653, 13567, 14033, 17291, 18353, 19181, 19457, 20021, 22943, 23561, 24179, 27059, 29063, 29753, 31151, 33301, 35153
OFFSET
1,1
LINKS
EXAMPLE
53 is in the sequence because it is prime, nextprime(53) = 59 and (53+59)/2 = 56 = 8*7, an oblong number.
MATHEMATICA
f[n_] := NextPrime[n*(n + 1), -1] ; f /@ Select[Range[200], (ob = #*(# + 1)) == (NextPrime[ob, -1] + NextPrime[ob])/2 &] (* Amiram Eldar, May 06 2020 *)
Select[Partition[Prime[Range[4000]], 2, 1], OddQ[Sqrt[1+4*Mean[#]]]&][[All, 1]] (* Harvey P. Dale, Oct 25 2020 *)
PROG
(PARI){for(i=3, 10^5, if(isprime(i), k=(i+nextprime(i+1))/4; if(issquare(8*k+1), print1(i, ", "))))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Antonio Roldán, May 12 2014
STATUS
approved