|
Search: id:A096265
|
|
|
| A096265 |
|
Aloof primes: Total distance between prime and neighboring primes sets record. |
|
+0
2
|
|
| 2, 3, 5, 7, 23, 53, 89, 113, 211, 1129, 1327, 2179, 2503, 5623, 9587, 14107, 19609, 19661, 31397, 31469, 38501, 58831, 155921, 360749, 370261, 396833, 1357201, 1561919, 4652353, 8917523, 20831323, 38089277, 70396393, 72546283, 102765683
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
EXAMPLE
|
a(1) = 2 as 2 has only one prime neighbor, 3, and 3-2 = 1, the first possible
record. a(2) = 3 because the sum of the distances (gaps) from 3 to its two
neighboring primes is 3-2 + 5-3 = 3 > 1, beating the previous record. a(5) = 23
because 23, with 29-19 = 10, is the smallest prime beating a(4) = 7's 11-5 = 6.
|
|
MATHEMATICA
|
PrimeNextDelta[n_]:=(Do[If[PrimeQ[n+k], a=n+k; d=a-n; Break[]], {k, 9!}]; d); PrimePrevDelta[n_]:=(Do[If[PrimeQ[n-k], a=n-k; d=n-a; Break[]], {k, n}]; d); q=0; lst={2}; Do[p=Prime[n]; d1=PrimeNextDelta[p]; d2=PrimePrevDelta[p]; d=d1+d2; If[d>q, AppendTo[lst, p]; q=d], {n, 2, 10^4}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Aug 07 2008]
|
|
PROGRAM
|
(PARI) /* 436272953 is the next-to-the-largest precalculated prime */
/* with which PARI/GP (Version 2.0.17 (beta) at least) can be started */
/* A different program would be required to go beyond a(37)=325737821 */
{r=0; print1("2, "); forprime(p=3, 436272953,
s=nextprime(p+1)-precprime(p-1); if(s>r, print1(p, ", "); r=s))}
|
|
CROSSREFS
|
Cf. A031132 (record distances corresponding to a(2) onward), A023186 (Lonely primes), A087770 (Lonely primes, another definition).
Sequence in context: A059170 A068710 A120805 this_sequence A056041 A083017 A052087
Adjacent sequences: A096262 A096263 A096264 this_sequence A096266 A096267 A096268
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Rick L. Shepherd (rshepherd2(AT)hotmail.com), Jun 21 2004
|
|
|
Search completed in 0.002 seconds
|
