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A262935 Increasing distances of lonely twin primes pairs to nearest prime. 1
1, 2, 4, 6, 10, 12, 16, 18, 28, 30, 34, 42, 46, 48, 58, 88, 90, 94, 124, 130, 136, 154, 162, 168, 172, 178, 202, 216, 258, 264, 294, 342, 352, 354, 364, 366, 370, 378, 396, 408 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..40.

FORMULA

a(n) = d if ( (p(i+1) = p(i)+2) AND (d = min(p(i+2)-p(i+1), p(i)-p(i-1)) > a(n-1)) ), where a(0) = 0, p(k) = prime(k) = A000040(k).

EXAMPLE

(3,5) is a twin primes pair, min(7-5, 3-2)=1, therefore a(1)=1.

(5,7) is a twin primes pair, min(11-7, 5-3)=2>1, therefore a(2)=2.

(11,13) is a twin primes pair, min(17-13, 11-7)=4>2, therefore a(3)=4.

PROG

(PARI) {m=0; q=5; s=3; t=2; forprime(p=6, 10^9, if((q-s==2) && (min(p-q, s-t)>m), m=min(p-q, s-t); print1(m, ", ") ); t=s; s=q; q=p; )}

CROSSREFS

Cf. A035789, A069453, A069455, A262936.

Sequence in context: A006093 A127965 A117891 * A178539 A072752 A036634

Adjacent sequences:  A262932 A262933 A262934 * A262936 A262937 A262938

KEYWORD

nonn

AUTHOR

Dmitry Petukhov, Oct 04 2015

STATUS

approved

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Last modified November 12 22:01 EST 2019. Contains 329079 sequences. (Running on oeis4.)