A051395 Numbers whose square is a sum of 4 consecutive primes.

6, 18, 24, 42, 48, 70, 144, 252, 258, 358, 378, 388, 396, 428, 486, 506, 510, 558, 608, 644, 864, 886, 960, 974, 1022, 1046, 1326, 1362, 1392, 1398, 1422, 1434, 1442, 1468, 1476, 1592, 1604, 1676, 1820, 1950, 2016, 2068, 2140, 2288, 2430, 2460

Offset

1,1

Comments

First of four consecutive primes in A206280.

Links

Charles R Greathouse IV and Zak Seidov, Table of n, a(n) for n = 1..10783 (First 3400 terms from Charles R Greathouse IV)

Formula

Numbers m such that m^2 = Sum_{i=k..k+3} prime(i) for some k.

Example

6 is a term because 6*6 = 5 + 7 + 11 + 13;
18 is a term because 18*18 = 324 = 73 + 79 + 83 + 89.

Prog

(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
(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

Crossrefs

Cf. A072849, A206280.

Sequence in context: A028887 A283118 A274536 * A256266 A228104 A028558

Adjacent sequences: A051392 A051393 A051394 * A051396 A051397 A051398

Keyword

easy,nonn

Author

Zak Seidov, Jun 21 2003

Extensions

Corrected and extended by Don Reble, Nov 20 2006

Status

approved