login
A051395
Numbers whose square is a sum of 4 consecutive primes.
12
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.
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
Sequence in context: A028887 A283118 A274536 * A256266 A228104 A028558
KEYWORD
easy,nonn
AUTHOR
Zak Seidov, Jun 21 2003
EXTENSIONS
Corrected and extended by Don Reble, Nov 20 2006
STATUS
approved