

A145898


Ending prime: where number of consecutive squares m^2 satisfy r = p + 4*m^2, prime.


2



37, 151, 29, 23, 293, 107, 263, 83, 113, 107, 113, 131, 1607, 197, 239, 233, 313, 311, 317, 353, 383, 401, 443, 461, 499, 523, 503, 617, 659, 677, 743, 773, 773, 887, 857, 863, 881, 887, 911, 953, 983, 1013, 1283, 1129, 1277, 1283, 1301, 1319, 1619, 1433
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OFFSET

1,1


COMMENTS

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.


LINKS



EXAMPLE

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).


PROG

(UBASIC)
10 'p464
20 N=1
30 A=3:S=sqrt(N)
40 B=N\A
50 if B*A=N then 100
60 A=A+2
70 if A<=S then 40
80 M=M+1:R=N+4*M^2:if R=prmdiv(R) and M<100 then print N; R; M:goto 80
90 if M>=1 then stop
100 M=0:N=N+2:goto 30


CROSSREFS



KEYWORD

easy,nonn


AUTHOR



STATUS

approved



