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

1,1

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

Example

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

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 *)

Prog

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

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.

Sequence in context: A143272 A153877 A229491 * A083494 A126857 A161348

Adjacent sequences: A263673 A263674 A263675 * A263677 A263678 A263679

Keyword

nonn,easy

Author

Antonio Roldán, Oct 23 2015

Status

approved