A069455
Greater of lonely twin primes.
Original entry on oeis.org
31, 43, 61, 73, 229, 241, 271, 283, 313, 349, 463, 523, 571, 601, 619, 643, 661, 859, 883, 1093, 1153, 1231, 1279, 1291, 1303, 1321, 1429, 1453, 1609, 1621, 1669, 1699, 1723, 1789, 1999, 2029, 2143, 2239, 2269, 2311, 2341, 2383
Offset: 1
The first lonely twin primes (A069453) are 29,31 (23 and 37 are non-twin), 41,43 (37 and 47 are non-twin), 59,61 (53 and 67 are non-twin). Of these, the greater twins are 31,43,61, so this is how the sequence begins.
A262936
Lesser of lonely twin primes pairs with increasing distance to nearest prime.
Original entry on oeis.org
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
(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.
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{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;)}
A259034
Start of a string of exactly 9 consecutive (but disjoint) pairs of twin primes.
Original entry on oeis.org
170669145704411, 597655503030737, 1209758169609917, 1529543606818727, 1980326398382819, 2752137854763287, 3748062700238369, 4071945430128767, 4518517172328671, 4662894516572177, 5979435335619701, 6264049608329957, 7609375387833677, 8064845880680819
Offset: 1
A262935
Increasing distances of lonely twin primes pairs to nearest prime.
Original entry on oeis.org
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
Offset: 1
(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.
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{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;)}
A069472
Smallest twin prime in a sequence of exactly n disjoint twin pairs, sandwiched between non-twins.
Original entry on oeis.org
29, 101, 179, 9419, 909287, 325267931, 678771479, 1107819732821, 170669145704411, 3324648277099157
Offset: 1
The first sequence of primes containing exactly 1 pair of twins, sandwiched between non-twins, is 29, 31. The first containing exactly 2 disjoint pairs similarly sandwiched is 101, 103, 107, 109. The first containing exactly 3 disjoint pairs similarly sandwiched is 179, 181, 191, 193, 197, 199. So the sequence starts 29, 101, 179.
More terms from Lévai Gábor (gablevai(AT)vipmail.hu), Jan 11 2005