

A096265


Aloof primes: Total distance between prime and neighboring primes sets record.


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
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OFFSET

1,1


LINKS

Hugo Pfoertner, Table of n, a(n) for n = 1..55, terms 1..50 from Ken Takusagawa.


EXAMPLE

a(1) = 2 as 2 has only one prime neighbor, 3 and 32 = 1, the first possible record. a(2) = 3 because the sum of the distances (gaps) from 3 to its two neighboring primes is 32 + 53 = 3 > 1, beating the previous record. a(5) = 23 because 23, with 2919 = 10, is the smallest prime beating a(4) = 7's 115 = 6.


MATHEMATICA

PrimeNextDelta[n_]:=(Do[If[PrimeQ[n+k], a=n+k; d=an; Break[]], {k, 9!}]; d); PrimePrevDelta[n_]:=(Do[If[PrimeQ[nk], a=nk; d=na; 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 (* Vladimir Joseph Stephan Orlovsky, Aug 07 2008 *)


PROG

(PARI) /* 436272953 is the nexttothelargest 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(p1); 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: A068710 A120805 A177119 * A056041 A083017 A006510
Adjacent sequences: A096262 A096263 A096264 * A096266 A096267 A096268


KEYWORD

nonn


AUTHOR

Rick L. Shepherd, Jun 21 2004


STATUS

approved



