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 A298272 The first of three consecutive hexagonal numbers the sum of which is equal to the sum of three consecutive primes. 6
 6, 6216, 7626, 9180, 16836, 19900, 22366, 29646, 76636, 89676, 93096, 114960, 116886, 118828, 322806, 365940, 397386, 422740, 437580, 471906, 499500, 574056, 595686, 626640, 690900, 743590, 984906, 1041846, 1148370, 1209790, 1260078, 1357128, 1450956 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 (first 100 terms from Colin Barker) EXAMPLE 6 is in the sequence because 6+15+28 (consecutive hexagonal numbers) = 49 = 13+17+19 (consecutive primes). MAPLE N:= 100: # to get a(1)..a(100) count:= 0: mmax:= floor((sqrt(24*N-87)-9)/12): for i from 1 while count < N do   mi:= 2*i;   m:= 6*mi^2+9*mi+7;   r:= ceil((m-8)/3);   p1:= prevprime(r+1);   p2:= nextprime(p1);   p3:= nextprime(p2);   while p1+p2+p3 > m do     p3:= p2; p2:= p1; p1:= prevprime(p1);   od:   if p1+p2+p3 = m then     count:= count+1;     A[count]:= mi*(2*mi-1);   fi od: seq(A[i], i=1..count); # Robert Israel, Jan 16 2018 PROG (PARI) L=List(); forprime(p=2, 2000000, q=nextprime(p+1); r=nextprime(q+1); t=p+q+r; if(issquare(24*t-87, &sq) && (sq-9)%12==0, u=(sq-9)\12; listput(L, u*(2*u-1)))); Vec(L) CROSSREFS Cf. A000040, A000384, A054643, A298073, A298168, A298169, A298222, A298223, A298250, A298251, A298273. Sequence in context: A111152 A202969 A003191 * A000438 A061109 A321983 Adjacent sequences:  A298269 A298270 A298271 * A298273 A298274 A298275 KEYWORD nonn AUTHOR Colin Barker, Jan 16 2018 STATUS approved

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Last modified May 22 04:12 EDT 2022. Contains 353933 sequences. (Running on oeis4.)