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

1,1

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.

Formula

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

Prog

(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); }

Crossrefs

Cf. A001097, A020639, A358657.

Sequence in context: A282000 A013785 A100509 * A013840 A253780 A134370

Adjacent sequences: A378262 A378263 A378264 * A378266 A378267 A378268

Keyword

nonn

Author

Amiram Eldar, Nov 21 2024

Status

approved