A349405 a(n) = A347113(A347313(n))+1.

95, 6, 15, 39, 14, 22, 119, 87, 57, 46, 123, 215, 159, 94, 93, 219, 74, 118, 122, 303, 142, 134, 327, 166, 695, 178, 395, 206, 214, 226, 447, 959, 262, 254, 543, 291, 302, 326, 334, 699, 346, 358, 382, 386, 394, 843, 1727, 879, 446, 454, 478, 482, 502, 8159, 514

Offset: 1

Author

Michael De Vlieger, Nov 16 2021

Keywords

• nonn

Comments

These numbers generate primes in A347113.

Let s = A347113, j = s(i)+1, and k = s(i+1). For prime k, j is a squarefree semiprime pq, p < q.

The first 3 primes in s have k = p, while all others observed for i <= 2^19 have k = q.

Examples

			a(1) = s(6)+1 = 95 -> s(7) = 5,
a(2) = s(7)+1 = 6 -> s(8) = 2,
a(3) = s(10)+1 = 15, -> s(11) = 3,
a(4) = s(18)+1 = 39, -> s(19) = 13, etc.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000
• Michael De Vlieger, Extended table of n, a(n) for n = 1..23082 (all terms resulting from 2^19 terms of A347113)
• Michael De Vlieger, Log-log scatterplot of A347113(n) n=1..256, indicating primes in green, labeling them with the value a(n) = A347113(n-1)+1. Red dots represent records A347307 in A347113, and blue represent local minima A347756 in A347113.

Crossrefs

Cf. A006530, A020639, A347113, A347313, A348779, A349406.

Programs

Mathematica

c[] = 0; j = m = 2; m = {1}~Join~Reap[Do[If[IntegerQ@ Log2[i], While[c[m] > 0, m++]]; Set[k, m]; While[Or[c[k] > 0, k == j, GCD[j, k] == 1], k++]; Sow[k]; Set[c[k], i]; j = k + 1, {i, 530}]][[-1, -1]]; m[[Position[m, ?PrimeQ][[All, 1]] - 1]] + 1