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%I #7 Feb 27 2023 07:45:52
%S 37,151,29,23,293,107,263,83,113,107,113,131,1607,197,239,233,313,311,
%T 317,353,383,401,443,461,499,523,503,617,659,677,743,773,773,887,857,
%U 863,881,887,911,953,983,1013,1283,1129,1277,1283,1301,1319,1619,1433
%N Ending prime: where number of consecutive squares m^2 satisfy r = p + 4*m^2, prime.
%C Farideh Firoozbakht noticed the unusually high number of 19 primes ending in a(13)=1607 in A145741 where she specified an m sequence of 1..10. My m sequence is open. 1,2,3,...,m+1, all squared.
%e a(1)=37 because when m is 3, the first prime is 5 and the ending prime is 37: r=1+4*1^1=5, prime; and r=1+4*2^2=17, prime; and r=1+4*3^2=37, prime (and the next value of r does not produce a prime).
%o (UBASIC)
%o 10 'p464
%o 20 N=1
%o 30 A=3:S=sqrt(N)
%o 40 B=N\A
%o 50 if B*A=N then 100
%o 60 A=A+2
%o 70 if A<=S then 40
%o 80 M=M+1:R=N+4*M^2:if R=prmdiv(R) and M<100 then print N;R;M:goto 80
%o 90 if M>=1 then stop
%o 100 M=0:N=N+2:goto 30
%Y Cf. A145896, A145897, A145741.
%K easy,nonn
%O 1,1
%A _Enoch Haga_, Oct 25 2008
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