A242383 Lesser of consecutive primes whose average is an oblong number.

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

Amiram Eldar, Table of n, a(n) for n = 1..10000

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

Cf. A002378, A154634, A263676.

Sequence in context: A019345 A279067 A049489 * A141785 A144311 A074367

Adjacent sequences: A242380 A242381 A242382 * A242384 A242385 A242386

Keyword

nonn

Author

Antonio Roldán, May 12 2014

Status

approved