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 A072330 Common difference n such that primitive triangles exist which are n-arithmetic (i.e., primitive Heronian triangles whose sides in arithmetic progression have common difference n). 8
 1, 11, 13, 23, 37, 47, 59, 61, 71, 73, 83, 97, 107, 109, 121, 131, 143, 157, 167, 169, 179, 181, 191, 193, 227, 229, 239, 241, 251, 253, 263, 277, 299, 311, 313, 337, 347, 349, 359, 373, 383, 397, 407, 409, 419, 421, 431, 433, 443, 457, 467, 479, 481, 491, 503 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The first entry in particular is associated with sequences A003500 and A007655. Such a triangle has a middle side 2*x partitioned into x +- 2*n by the corresponding altitude (i.e., median and altitude points are always a distance 2*n apart). LINKS Frank M Jackson, Table of n, a(n) for n = 1..10000 R. A. Beauregard and E. R. Suryanarayan, Arithmetic Triangles, Mathematics Magazine, pp. 105-115 70(2) 1997 MAA. FORMULA n = 1 or a product of primes p congruent to +- 1 (mod 12). MAPLE isA072330 := proc(n) if n = 1 then true; else for p in ifactors(n)[2] do if not modp(op(1, p), 12) in {1, 11} then return false ; end if; end do: true; end if; end proc: for n from 1 to 1000 do if isA072330(n) then printf("%d, ", n) ; end if; end do: # R. J. Mathar, Feb 26 2017 MATHEMATICA fac12Q[n_] := And @@ (MemberQ[{1, 11}, #] & /@ Mod[First /@ FactorInteger@ n, 12]); Select[Range[600], fac12Q] (* Frank M Jackson, Apr 09 2016 with simplification by Giovanni Resta *) okQ[n_] := AllTrue[FactorInteger[n][[All, 1]], MatchQ[Mod[#, 12], 1|11]&]; Select[Range[1000], okQ] (* Jean-François Alcover, Mar 06 2020 *) CROSSREFS Cf. A072360, A086909, A089019, A089020, A096672, A096673, A096674. Sequence in context: A048393 A136058 A106073 * A097933 A166484 A127043 Adjacent sequences: A072327 A072328 A072329 * A072331 A072332 A072333 KEYWORD nonn AUTHOR Lekraj Beedassy, Jul 15 2002 EXTENSIONS Corrected and extended by Ray Chandler, Jul 02 2004 Incorrect b-file by Carmine Suriano replaced by Frank M Jackson, May 09 2016 STATUS approved

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Last modified December 8 13:46 EST 2023. Contains 367679 sequences. (Running on oeis4.)