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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.

%I A246760 #15 Jul 28 2016 19:47:35
%S A246760 5,41,617,653,797,941,977,1013,1049,1193,1229,1373,1409,1553,1697,
%T A246760 1733,1877,1913,1949,2273,2309,2633,2777,3677,3821,4397,4721,5297,
%U A246760 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
%N 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.
%C A246760 All terms are congruent to 5 mod 36.
%C A246760 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
%H A246760 Harvey P. Dale, <a href="/A246760/b246760.txt">Table of n, a(n) for n = 1..1000</a>
%e A246760 41 - 5 = 6^2, 617 - 41 = 24^2, 653 - 617 = 6^2.
%t A246760 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 *)
%o A246760 (PARI) print1(p=5",");for(k=1,100,x=1;while(!isprime(q=p+36*x^2),x=x+1);print1(q",");p=q)
%Y A246760 Cf. A073609, A073770, A076201, A108022, A108023.
%K A246760 nonn
%O A246760 1,1
%A A246760 _Zak Seidov_, Sep 02 2014