A206281 Smallest of five consecutive primes whose sum is a square.

181, 199, 317, 3529, 3733, 4177, 4663, 9049, 15329, 15991, 19577, 24907, 43607, 47017, 58073, 84223, 86843, 146191, 152417, 156623, 175543, 217559, 227671, 288461, 308999, 323077, 331249, 333323, 354301, 390289, 397037, 407249, 474923, 476137, 491059, 520339

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..5000

Example

a(4) = 3529. The next four primes are 3533, 3539, 3541, and 3547, and the sum of all five primes = 17689 = 133^2.

Maple

count:= 0: Res:= NULL:
for y from 10 while count < 100 do
  target:= y^2;
  t:= prevprime(ceil(target/5));
  s:= prevprime(t);
  r:= prevprime(s);
  q:= prevprime(r);
  p:= prevprime(q);
  u:= p+q+r+s+t;
  while u < target do
    p:= q; q:= r; r:= s; s:= t; t:= nextprime(t);
    u:= p+q+r+s+t;
  od;
  if u = target then
     count:= count+1; Res:= Res, p;
  fi
od:
Res; # Robert Israel, Oct 20 2020

Mathematica

Transpose[Select[Partition[Prime[Range[80000]], 5, 1], IntegerQ[Sqrt[ Total[#]]]&]][[1]]

Crossrefs

Cf. A061275, A206279, A206280.

Sequence in context: A139649 A159263 A159548 * A224614 A216309 A139648

Adjacent sequences: A206278 A206279 A206280 * A206282 A206283 A206284

Keyword

nonn

Author

Harvey P. Dale, Feb 05 2012

Status

approved