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A051395 Numbers n such that n^2 is a sum of 4 consecutive primes. 11

%I

%S 6,18,24,42,48,70,144,252,258,358,378,388,396,428,486,506,510,558,608,

%T 644,864,886,960,974,1022,1046,1326,1362,1392,1398,1422,1434,1442,

%U 1468,1476,1592,1604,1676,1820,1950,2016,2068,2140,2288,2430,2460

%N Numbers n such that n^2 is a sum of 4 consecutive primes.

%C First of four consecutive primes in A206280.

%H Charles R Greathouse IV and Zak Seidov, <a href="/A051395/b051395.txt">Table of n, a(n) for n = 1..10783 (First 3400 terms from Charles R Greathouse IV)</a>

%F n such that n^2 = sum_{i=k..k+3} prime(i) for some k.

%e a(1)=6 because 6*6=5+7+11+13; a(2)=18 because 18*18=324=73+79+83+89.

%o (PARI) lista(nn) = {pr = primes(nn); for (i = 1, nn - 3, s = pr[i] + pr[i+1] + pr[i+2] + pr[i+3]; if (issquare(s), print1(sqrtint(s), ", ")););} \\ _Michel Marcus_, Oct 02 2013

%o (PARI) is(n)=n*=n; my(p=precprime(n\4),q=nextprime(n\4+1),r,s); if(n < 3*q+p+8, r=precprime(p-1); s=n-p-q-r; ispseudoprime(s) && (s == precprime(r-1) || s == nextprime(q+1)), r=nextprime(q+1); s=n-p-q-r; ispseudoprime(s) && (s == precprime(p-1) || s == nextprime(r+1))) \\ _Charles R Greathouse IV_, Oct 02 2013

%Y Cf. A072849, A206280.

%K easy,nonn

%O 1,1

%A _Zak Seidov_, Jun 21 2003

%E Corrected and extended by _Don Reble_, Nov 20 2006

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Last modified August 18 08:57 EDT 2019. Contains 326077 sequences. (Running on oeis4.)