A246760 a(1) = 5; a(n) for n > 1 is the smallest prime > a(n-1) that differs from a(n-1) by a square.

5, 41, 617, 653, 797, 941, 977, 1013, 1049, 1193, 1229, 1373, 1409, 1553, 1697, 1733, 1877, 1913, 1949, 2273, 2309, 2633, 2777, 3677, 3821, 4397, 4721, 5297, 5333, 5477, 5801, 6701, 6737, 8501, 8537, 8573, 8609, 8753, 11057, 11093, 13397, 13721, 13757, 13901, 18257, 18401, 19301, 20201, 21101, 22397, 22433, 22469, 22613, 22937, 22973, 23117, 24413, 24989

Offset: 1

Author

Zak Seidov, Sep 02 2014

Keywords

• nonn

Comments

All terms are congruent to 5 mod 36.

For sequences of this type, once you get a(n) == 5, 11, 17, 23, 29, or 35 mod 36, all later terms stay in the same congruence class mod 36. Sequences in the same congruence class are likely to merge after a few terms. Thus with a(1) = 77 you get 77, 113, 149, 293, 617 and from then on it's the same as the present sequence. - Robert Israel, Sep 05 2014

Examples

			41 - 5 = 6^2, 617 - 41 = 24^2, 653 - 617 = 6^2.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A073609, A073770, A076201, A108022, A108023.

Programs

Mathematica

sps[n_]:=Module[{p=NextPrime[n]},While[!IntegerQ[Sqrt[p-n]],p= NextPrime[ p]];p]; NestList[sps,5,60] (* Harvey P. Dale, Jul 28 2016 *)

PARI

print1(p=5",");for(k=1,100,x=1;while(!isprime(q=p+36*x^2),x=x+1);print1(q",");p=q)