A092950 Beginning with n, add the next number, subtract the previous number and so on until one gets a prime, or 0 if no such prime is reached in 2n-1 steps: a(n) = n + (n+1) - (n-1) +(n+2) -(n-2) +(n+3)-(n-3)...+...is the first occurring prime at any step.

3, 2, 3, 17, 5, 13, 7, 17, 19, 29, 11, 73, 13, 29, 31, 41, 17, 37, 19, 41, 43, 53, 23, 73, 31, 53, 29, 137, 29, 61, 31, 73, 67, 149, 71, 73, 37, 101, 79, 89, 41, 109, 43, 89, 47, 101, 47, 97, 107, 101, 103, 113, 53, 109, 61, 113, 59, 197, 59, 241, 61, 149, 127, 137, 131, 157

Offset

1,1

Comments

a(p) = p, p is a prime. If the process is continued until a 1 is subtracted the result is n^2. Conjecture: No term is zero.

Links

Table of n, a(n) for n=1..66.

Formula

The k-th step of the process used to generate the n-th term is 2n+(k^2)/4 if k is even and n+(k^2-1)/4 if k is odd. - Adam M. Kalman (mocha(AT)clarityconnect.com), Nov 09 2004

Example

a(4) = 17 and the steps are 4, 4+5, 4+5-3, 4+5-3+6, 4+5-3+6-2, 4+5-3+6-2+7= 17. a(6) = 6+7 =13.

Mathematica

For[a=1, a<100, x:=a; s:=1; While[(!PrimeQ[x])\[And](s<=2a-1), If[OddQ[s], x+=a+(s+1)/2, x+=-a+s/2]; s++ ]; If[PrimeQ[x], Print[x], Print[0]]; a++ ]; (Kalman)

Crossrefs

Cf. A092951, A092952.

Sequence in context: A247237 A059366 A298594 * A059239 A350517 A123170

Adjacent sequences: A092947 A092948 A092949 * A092951 A092952 A092953

Keyword

nonn

Author

Amarnath Murthy, Mar 24 2004

Extensions

More terms from Adam M. Kalman (mocha(AT)clarityconnect.com), Nov 09 2004

Status

approved