A145896 Values of m: where m^2 begins a run of consecutive squares satisfying r=p+4*m^2 with a sequence of primes.

3, 6, 2, 1, 8, 4, 7, 1, 2, 1, 1, 1, 19, 1, 2, 1, 3, 1, 1, 1, 1, 1, 1, 1, 3, 3, 1, 1, 2, 1, 1, 2, 1, 4, 1, 1, 1, 1, 1, 2, 2, 1, 7, 3, 4, 1, 1, 2, 7, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2

Offset: 1

Author

Enoch Haga, Oct 25 2008

Keywords

• easy
• nonn

Comments

Suggested by Farideh Firoozbakht's Puzzle 464 in Carlos Rivera's The Prime Puzzles & Problems Connection

Examples

			a(1)=3 because when m is 3 a sequence of three values of r end with prime 37; then 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 m, 4, does not produce a prime because r=1+4*4^2=65). For this one value 1 is assumed prime.
		

Crossrefs

A145897 A145898 A145741

Programs

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