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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Ken Takusagawa, Table of n, a(n) for n = 1..50

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 (* Vladimir Joseph Stephan Orlovsky, Aug 07 2008 *)

PROG

(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: 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

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Last modified November 13 07:13 EST 2019. Contains 329085 sequences. (Running on oeis4.)