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A263676
Numbers that are both interprime and oblong.
4
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
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.
Sequence in context: A143272 A153877 A229491 * A083494 A126857 A161348
KEYWORD
nonn,easy
AUTHOR
Antonio Roldán, Oct 23 2015
STATUS
approved