A214265 First primes beginning a chain of 4 primes indexed equidistantly (n-th, (n+b)-th, (n+2b)-th, (n+3b)-th primes) whose sum of squares is the square of two times a prime and with b <= n.

137, 199, 223, 773, 2161, 2477, 3943, 4079, 4423, 4603, 6791, 7297, 7547, 7559, 12853, 15299, 17431, 20807, 22573, 22637, 25931, 27179, 31337, 32027, 32303, 34403, 36683, 37573, 38501, 38671, 41549, 45523, 48193, 51941, 57689, 58679, 60913, 61471, 61483

Offset

1,1

Comments

Note that 61471 and 61483 are consecutive primes; 65537 = 2^16+1 .The lowest indexed equidistance up to n=500000, is b=4 for n=46, p(46) = 199.

Links

Table of n, a(n) for n=1..39.

Example

199^2 + 229^2 + 251^2 + 271^2 = 478^2 and 239 is prime; b = 4.
137^2 + 223^2 + 307^2 + 397^2 = 566^2 and 283 is prime; b = 15.
223^2 + 307^2 + 397^2 + 487^2 = 734^2 and 367 is prime; b = 15.
11^2 + 59^2 + 109^2 + 179^2 = 218^2 and 109 is prime; was not included because p(5) = 11 and b = 12 > 5.

Prog

(PARI) for(n=1, 10000, for(b=1, n, a=(prime(n))^2+(prime(n+b))^2+(prime(n+2*b))^2+ (prime(n+3*b))^2; if(issquare(a)&isprime(sqrtint(a)/2), print1(prime(n)", "))))

Crossrefs

Sequence in context: A356980 A139510 A142651 * A327450 A142135 A142257

Adjacent sequences: A214262 A214263 A214264 * A214266 A214267 A214268

Keyword

nonn

Author

Robin Garcia, Jul 09 2012

Status

approved