A298222 - OEIS

A298222

The first of three consecutive squares the sum of which is equal to the sum of three consecutive primes.

1444, 5776, 6400, 9604, 10816, 13924, 14400, 14884, 22500, 28900, 36100, 61504, 62500, 67600, 88804, 115600, 136900, 166464, 211600, 232324, 291600, 315844, 425104, 454276, 577600, 602176, 715716, 817216, 937024, 1016064, 1020100, 1290496, 1397124, 1507984

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OFFSET

1,1

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..750 (* First 100 terms from Colin Barker. *)

EXAMPLE

1444 is in the sequence because 1444+1521+1600 (consecutive squares) = 4565 = 1511+1523+1531 (consecutive primes).

MATHEMATICA

p3Q[{a_, b_, c_}]:=With[{pf=PrimePi[NextPrime[a]], pl=PrimePi[NextPrime[c, -1]]}, MemberQ[Total/@Partition[Prime[Range[pf, pl]], 3, 1], a+b+c]]; Select[ Partition[ Range[ 2000]^2, 3, 1], p3Q][[;; , 1]] (* Harvey P. Dale, Oct 10 2025 *)

Select[(Sqrt[3] Sqrt[#-2]-3)/3&/@Total/@Partition[Prime[Range[150000]], 3, 1], IntegerQ]^2 (* Harvey P. Dale, Jan 03 2026 *)

PROG

(PARI) L=List(); forprime(p=2, 400000, q=nextprime(p+1); r=nextprime(q+1); t=p+q+r; if(issquare(12*t-24, &sq) && (sq-6)%6==0, u=(sq-6)\6; listput(L, u^2))); Vec(L)

CROSSREFS

Cf. A000040, A000290, A054643, A298073, A298168, A298169, A298223.

Sequence in context: A105417 A105416 A348740 * A374267 A180465 A328886

Adjacent sequences: A298219 A298220 A298221 * A298223 A298224 A298225

KEYWORD

nonn

AUTHOR

Colin Barker, Jan 15 2018

STATUS

approved