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%I #19 Oct 25 2020 17:18:39
%S 5,11,29,41,53,71,239,337,419,461,503,547,599,647,863,1051,1187,1481,
%T 1721,1801,2549,2647,2969,3539,4421,6317,7129,8009,10301,12653,13567,
%U 14033,17291,18353,19181,19457,20021,22943,23561,24179,27059,29063,29753,31151,33301,35153
%N Lesser of consecutive primes whose average is an oblong number.
%H Amiram Eldar, <a href="/A242383/b242383.txt">Table of n, a(n) for n = 1..10000</a>
%e 53 is in the sequence because it is prime, nextprime(53) = 59 and (53+59)/2 = 56 = 8*7, an oblong number.
%t f[n_] := NextPrime[n*(n + 1), -1] ; f /@ Select[Range[200], (ob = #*(# + 1)) == (NextPrime[ob, -1] + NextPrime[ob])/2 &] (* _Amiram Eldar_, May 06 2020 *)
%t Select[Partition[Prime[Range[4000]],2,1],OddQ[Sqrt[1+4*Mean[#]]]&][[All,1]] (* _Harvey P. Dale_, Oct 25 2020 *)
%o (PARI){for(i=3,10^5,if(isprime(i),k=(i+nextprime(i+1))/4;if(issquare(8*k+1),print1(i,", "))))}
%Y Cf. A002378, A154634, A263676.
%K nonn
%O 1,1
%A _Antonio Roldán_, May 12 2014
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