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A378265 Terms k of A358657 such that lpf(k-1) and lpf(k+1) are twin primes pair, where lpf(k) = A020639(k) is the least prime dividing k.

%I A378265 #12 Apr 26 2025 01:44:32
%S A378265 216,1591596,2046456,2051496,3108204,8933184,10496844,10630836,
%T A378265 13579236,20866644,26666856,27288036,30398544,30538404,33949656,
%U A378265 34851384,35722044,36657180,38588544,48634956,67747896,81982116,82130796,87172884,87865056,98639100,100473444
%N A378265 Terms k of A358657 such that lpf(k-1) and lpf(k+1) are twin primes pair, where lpf(k) = A020639(k) is the least prime dividing k.
%C A378265 Iannucci (2004-2005) called the three numbers before each term and the three numbers after each term (i.e., {k-3, k-2, k-1} and {k+1, k+2, k+3}) "almost prime twin prime triplet twins" (APTPTTs for short), and found that there are 126 terms below 10^9.
%H A378265 Amiram Eldar, <a href="/A378265/b378265.txt">Table of n, a(n) for n = 1..10000</a>
%H A378265 Douglas E. Iannucci, <a href="https://www.proquest.com/docview/89065926">Almost prime twin prime triplet twins</a>, Journal of Recreational Mathematics, Vol. 33, No. 2 (2004-2005), pp. 125-129.
%F A378265 a(n) == 0 (mod 36). - _Hugo Pfoertner_, Nov 21 2024
%o A378265 (PARI) lista(lim) = {my(p = 2, f1, f2); forprime(q = 3, lim/2, if(q == p+2 && factor(2*p-1)[,2] == [1,1]~ && factor(2*q+1)[,2] == [1,1]~, f1 = factor(2*p+1); f2 = factor(2*q-1); if(f1[,2] == [1,1]~ && f2[,2] == [1,1]~ && abs(f1[1,1] - f2[1,1]) ==  2, print1(2*p+2, ", "))); p = q);}
%Y A378265 Cf. A001097, A020639, A358657.
%K A378265 nonn
%O A378265 1,1
%A A378265 _Amiram Eldar_, Nov 21 2024