A109926 Least k such that k-2^r is prime for n values of r. Index of the first occurrence of n in A109925.

1, 3, 4, 15, 21, 45, 75, 465, 1095, 2145, 4935, 14955, 80685, 229845, 1295325, 1575285, 9700575, 20435415, 15054105, 53999715, 2282745465

Offset

0,2

Comments

It appears that 3 and 5 divide a(n) for n>4. Note that a(18)<a(17). - T. D. Noe, Jul 19 2005

Conjecture: a(n)==0 (mod 3) for n > 2. Then n-2^k is not == 0 (mod 3) and a prime is more probable. - Robert G. Wilson v, Jul 21 2005

Conjecture: a(n+15)==0 (mod 30) for n > 4. - Robert G. Wilson v, Jul 21 2005

a(n) > 10^10 for n >= 21. - Donovan Johnson, Jan 21 2009

Links

Table of n, a(n) for n=0..20.

Example

a(4) = 21, 21-2 =19, 21-4 = 17, 21-8 = 13, 21-16 = 5, 21 is the smallest number that gives four such primes.

Mathematica

t=Table[cnt=0; r=1; While[r<n, If[PrimeQ[n-r], cnt++ ]; r=2r]; cnt, {n, 250000}]; Table[First[Flatten[Position[t, n]]], {n, 13}] (Noe)
f[n_] := Count[ PrimeQ[n - 2^Range[0, Floor[ Log[2, n]]]], True]; t = Table[0, {30}]; Do[ a = f[n]; If[ t[[a+1]] == 0, t[[a+1]] = n], {n, 4*10^8}]; t (* Robert G. Wilson v *)

Crossrefs

Cf. A109925.

Sequence in context: A041819 A369910 A095799 * A272514 A065942 A369082

Adjacent sequences: A109923 A109924 A109925 * A109927 A109928 A109929

Keyword

hard,more,nonn

Author

Amarnath Murthy, Jul 17 2005

Extensions

Edited, corrected and extended by T. D. Noe and Robert G. Wilson v, Jul 19 2005

a(20) from Donovan Johnson, Jan 21 2009

Status

approved