A262935 -id:A262935 - cp's OEIS frontend

A262936 Lesser of lonely twin primes pairs with increasing distance to nearest prime.

3, 5, 11, 29, 419, 521, 1931, 6449, 10007, 28349, 107507, 173429, 569321, 913637, 1349531, 3593201, 18286391, 80528741, 83528411, 591792347, 1971409091, 2061246347, 8579208791, 13861166687, 15250041281, 27034148369, 27066034997, 54125499299, 315361055237

Offset: 1

Dmitry Petukhov, Oct 04 2015

nonn

			(3,5) is a twin primes pair, min(7-5, 3-2)=1, therefore a(1)=3.
(5,7) is a twin primes pair, min(11-7, 5-3)=2>1, therefore a(2)=5.
(11,13) is a twin primes pair, min(17-13, 11-7)=4>2, therefore a(3)=11.

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

Subsequence of A001359.

Cf. A035789, A262935, A347280.

{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(s, ", ") ); t=s; s=q; q=p;)}

a(n) = p(i) if ( (p(i+1) = p(i)+2) AND (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).

A347280 Let P1>3, P2, P3, P4 be 4 consecutive primes with P3-P2 = 2. a(n) = P2 is the earliest occurrence of the 4-tuple with min(P2-P1, P4-P3) = 2*n, or 0 if no such constellation exists.

Original entry on oeis.org

11, 29, 0, 419, 521, 0, 1931, 6449, 0, 10037, 43541, 0, 10007, 28349, 0, 107507, 280409, 0, 261167, 173429, 0, 569321, 913637, 0, 1598447, 1789091, 0, 1349531, 5317451, 0, 17282051, 25844561, 0, 10851161, 28582787, 0, 36126917, 14318657, 0, 60117947, 42062717

Offset: 2

Hugo Pfoertner, Sep 03 2021

nonn

The "irregular" constellation 3, 5, 7, 11 is intentionally excluded.

			a(2) = 11, because min(11-7, 17-13) = 4 is the earliest occurrence of the minimum gap of 2*2 = 4 adjacent to a pair of twin primes.
a(3) = 29: the constellation 23, 29, 31, 37 has min(29-23, 37-31) = 2*3 = 6, whereas the preceding constellations 7, 11, 13, 19, and 13, 17, 19, 23 don't yield a minimum of 6.
a(5) = 419: 409, 419, 421, 431 leads to the earliest occurrence of the minimum adjacent gap of 2*5.

Hugo Pfoertner, Table of n, a(n) for n = 2..113

Subset of A001359.

Cf. A262935, A262936.

cp's OEIS Frontend

A262936 Lesser of lonely twin primes pairs with increasing distance to nearest prime.

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