|
Search: id:A152073
|
|
|
| A152073 |
|
a(n) = largest prime < p(n) such that p(n) - a(n) is a power of 2, where p(n) is the nth prime; a(n) = 0 if no such prime exists. |
|
+0
2
|
|
| 2, 3, 5, 7, 11, 13, 17, 19, 13, 29, 29, 37, 41, 43, 37, 43, 59, 59, 67, 71, 71, 79, 73, 89, 97, 101, 103, 107, 109, 0, 127, 73, 137, 0, 149, 149, 131, 163, 157, 163, 179, 127, 191, 193, 197, 179, 191, 223, 227, 229, 223, 239, 0, 241, 199, 13, 269, 269, 277, 281, 277, 179
(list; graph; listen)
|
|
|
OFFSET
|
2,1
|
|
|
COMMENT
|
a(n) = 0 for odd primes p(n) appearing in A065381.
Primes p(n) for which there is no such prime a(n) (in which case a(n)=0) are listed in A065381 = (2,127,149,251,331,337,373,...). [From M. F. Hasler (MHasler(AT)univ-ag.fr), Nov 23 2008]
|
|
LINKS
|
Leroy Quet, Home Page (listed in lieu of email address)
|
|
EXAMPLE
|
Looking at the primes less than the 10th prime = 29: 29 - 23 = 6, not a power of 2. 29-19 = 10, not a power of 2. 29-17 = 12, not a power of 2. But 29-13 = 16, a power of 2. Since p = 13 is the largest prime p such that 29 - p = a power of 2, then a(10) = 13.
|
|
PROGRAM
|
(PARI) A152073(n)={ local( q=n=prime(n)); while( q=precprime(q-1), n-q==1<<valuation(n-q, 2) & return(q)) } [From M. F. Hasler (MHasler(AT)univ-ag.fr), Nov 23 2008]
|
|
CROSSREFS
|
Cf. A065381, A139758, A152075, A152076.
Sequence in context: A100546 A117094 A074721 this_sequence A117289 A106317 A152242
Adjacent sequences: A152070 A152071 A152072 this_sequence A152074 A152075 A152076
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Leroy Quet Nov 23 2008
|
|
EXTENSIONS
|
Edited and extended by M. F. Hasler (MHasler(AT)univ-ag.fr) and Ray Chandler (rayjchandler(AT)sbcglobal.net), Nov 23 2008
|
|
|
Search completed in 0.002 seconds
|
