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A214735 Primes such that no pairwise sum is a square. 3
2, 3, 5, 17, 29, 37, 41, 43, 53, 67, 73, 89, 109, 113, 131, 137, 149, 151, 157, 163, 181, 197, 199, 229, 233, 241, 277, 293, 313, 317, 331, 337, 349, 367, 373, 389, 401, 409, 421, 433, 449, 457, 461, 521, 541, 557, 577, 593, 601, 613, 617, 619, 631, 641, 643 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n+1) is the smallest prime p > a(n) such that none of sums a(i)+p, i=1..n is a square.

The sequence is infinite.

LINKS

Zak Seidov, Table of n, a(n) for n = 1..10000

EXAMPLE

a(3) = 5 because 2 + 5 = 7 (not a square) and 3 + 5 = 8 (a cube, not a square).

7 is not in the sequence because 2 + 7 = 3^2. With 11, we have 11 + 5 = 4^2, and for 13, there is 3 + 13 = 4^2.

a(4) = 17, as 2 + 17 = 19 (a prime), 3 + 17 = 20 (divisible by a square but not itself a square) and 5 + 17 = 22 (a squarefree semiprime).

MATHEMATICA

t = {2}; currPrime = 2; len = 1; maxLen = 100; Do[Label[ne]; currPrime = NextPrime[currPrime]; Do[If[IntegerQ[Sqrt[t[[i]] + currPrime]], Goto[ne]], {i, len}]; AppendTo[t, currPrime]; len++, {maxLen - 1}]; t

PROG

(PARI) list(lim)=my(v=List([2])); forprime(p=3, lim, if(issquare(p+2), next); for(k=sqrtint(p+2)+1, sqrtint(2*p-2), if(setsearch(v, k^2-p), next(2))); listput(v, p)); Vec(v) \\ Charles R Greathouse IV, Feb 14 2017

CROSSREFS

Cf. A086086, A203988.

Sequence in context: A065725 A057468 A127062 * A216061 A029972 A077498

Adjacent sequences:  A214732 A214733 A214734 * A214736 A214737 A214738

KEYWORD

nonn

AUTHOR

Zak Seidov, Jul 27 2012

STATUS

approved

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Last modified July 22 03:22 EDT 2017. Contains 289648 sequences.