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
Examples
6 is a term because 6*6 = 5 + 7 + 11 + 13; 18 is a term because 18*18 = 324 = 73 + 79 + 83 + 89.
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)
Programs
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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
Formula
Numbers m such that m^2 = Sum_{i=k..k+3} prime(i) for some k.
Extensions
Corrected and extended by Don Reble, Nov 20 2006
Comments