A073755 Number of steps needed to reach a prime when the following map is repeatedly applied to n: if n is even then 2n + int(sqrt(n)) + 1, otherwise 2n - int(sqrt(n)) - 1; or -1 if no prime is ever reached.

10, 2, 1, 1, 9, 1, 1, 4, 2, 2, 5, 28, 3, 8, 1, 1, 1, 17, 2, 1, 27, 1, 1, 34, 7, 2, 4, 12, 4, 3, 2, 16, 2, 2, 1, 1, 1, 1, 12, 4, 9, 1, 33, 1, 6, 12, 1, 26, 2, 16, 11, 5, 21, 4, 2, 2, 6, 8, 15, 2, 3, 6, 1, 11, 3, 27, 2, 4, 1, 15, 2, 1, 1, 3, 12, 2, 2, 1, 8, 2, 7, 3, 6, 3, 16, 11, 4, 2, 25, 8, 4, 10

Offset: 2

Author

Felice Russo, Sep 02 2002

Keywords

• easy
• nonn

Examples

			For n=3, a(3)=2 because 3 -> 4 -> 11
		

Links

• Sean A. Irvine, Table of n, a(n) for n = 2..1000

Programs

UBASIC

10 cls
30 for I=2 to 100
32 H=I
40 if odd(H)=1 then goto 90 else goto 50
50 A=2*H+int(sqrt(H))+1:K=K+1
60 if prmdiv(A)=A then print I,K:goto 120
65 if K>1000 then print I,0:goto 120
70 H=A:goto 40
90 A=2*H-int(sqrt(H))-1:K=K+1
100 if prmdiv(A)=A then print I,K:goto 120
105 if K>1000 then print I,0:goto 120
110 H=A:goto 40
120 K=0
130 next