A178825 a(1) = 1, a(n+1) = least prime p > a(n) such that a(n) + p is a square.

1, 3, 13, 23, 41, 59, 137, 263, 313, 587, 709, 2207, 2417, 2767, 4289, 4547, 5857, 8543, 9413, 9631, 18593, 20611, 45953, 50147, 52253, 55331, 58913, 62191, 67409, 69491, 82609, 98867, 100049, 102451, 157649, 171827, 173917, 215459, 220141

Offset

1,2

Links

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

Formula

a(1) = 1, a(n+1) = MIN{p in A000040 >= a(n) such that a(n) + p is in A000290}.

Example

a(1) = 1 by definition.
a(2) = 3 as 3 is prime and 1 + 3 = 4 = 2^2.
a(3) = 13 as 13 is prime and 3 + 13 = 16 = 4^2.
a(4) = 23 as 23 is prime and 13 + 23 = 36 = 6^2.

Mathematica

lps[n_]:=Module[{p=NextPrime[n]}, While[!IntegerQ[Sqrt[n+p]], p= NextPrime[ p]]; p]; NestList[lps, 1, 40] (* Harvey P. Dale, Sep 07 2020 *)

Prog

(PARI) {print1(1, ", "); p=1; a=1; for(i=1, 10^4, p=nextprime(p+1); if(issquare(a+p), print1(p, ", "); a=p))}

Crossrefs

Cf. A000040, A000290, A083016 Rearrangement of primes such that the sum of two consecutive terms is a square.

Cf. A062064 (case a(1)=2). - Zak Seidov, Oct 11 2014

Sequence in context: A367296 A018709 A121756 * A147473 A030431 A090146

Adjacent sequences: A178822 A178823 A178824 * A178826 A178827 A178828

Keyword

nonn,easy

Author

Jonathan Vos Post, Dec 27 2010

Status

approved