A263676 Numbers that are both interprime and oblong.

6, 12, 30, 42, 56, 72, 240, 342, 420, 462, 506, 552, 600, 650, 870, 1056, 1190, 1482, 1722, 1806, 2550, 2652, 2970, 3540, 4422, 6320, 7140, 8010, 10302, 12656, 13572, 14042, 17292, 18360, 19182, 19460, 20022, 22952, 23562, 24180, 27060, 29070, 29756, 31152, 33306, 35156, 35532, 39006

Offset: 1

Author

Antonio Roldán, Oct 23 2015

Keywords

• nonn
• easy

Examples

			342 is in this sequence because 342 = 18*19 is oblong, and 342 = (337 + 347)/2, with 337 and 347 consecutive primes.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Interprime
• Eric Weisstein's World of Mathematics, Pronic Number

Crossrefs

Intersection of A024675 and A002378. - Omar E. Pol, Oct 24 2015

Lesser of consecutive primes is in the sequence A242383.

Cf. A075190, A075277, A075296, A078443, A130178, A263674, A263675.

Programs

Mathematica

lim = 40000; Intersection[Plus @@@ Partition[Table[Prime@ n, {n, 2, PrimePi@ lim}], 2, 1]/2, Table[n (n + 1), {n, 0, lim}]] (* Michael De Vlieger, Nov 18 2015, after Clark Kimberling at A024675 and Robert G. Wilson v at A002378 *)
obQ[n_]:=With[{divs=Partition[Divisors[n],2,1]},Length[Select[divs,#[[2]]-#[[1]]== 1 && Times@@#==n&]]>0]; Select[Mean/@Partition[Prime[ Range[ 2,40000]],2,1],obQ] (* Harvey P. Dale, Nov 01 2022 *)

PARI

{for(i=1,500,n=i*(i+1);if(n==(precprime(n-1)+nextprime(n+1))/2, print1(n,", ")))}