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

2,1

Links

Table of n, a(n) for n=2..93.

Example

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

Prog

(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

Crossrefs

Sequence in context: A057603 A040097 A010174 * A010173 A357339 A259712

Adjacent sequences: A073752 A073753 A073754 * A073756 A073757 A073758

Keyword

easy,nonn

Author

Felice Russo, Sep 02 2002

Status

approved