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.

216, 1591596, 2046456, 2051496, 3108204, 8933184, 10496844, 10630836, 13579236, 20866644, 26666856, 27288036, 30398544, 30538404, 33949656, 34851384, 35722044, 36657180, 38588544, 48634956, 67747896, 81982116, 82130796, 87172884, 87865056, 98639100, 100473444

Offset: 1

Author

Amiram Eldar, Nov 21 2024

Keywords

• nonn

Comments

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.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Douglas E. Iannucci, Almost prime twin prime triplet twins, Journal of Recreational Mathematics, Vol. 33, No. 2 (2004-2005), pp. 125-129.

Crossrefs

Cf. A001097, A020639, A358657.

Programs

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);}

Formula

a(n) == 0 (mod 36). - Hugo Pfoertner, Nov 21 2024