A352929 Indices of primes in A093714.

2, 3, 4, 6, 8, 10, 13, 15, 17, 24, 28, 32, 36, 38, 42, 52, 54, 58, 64, 66, 70, 72, 78, 85, 89, 97, 99, 101, 103, 107, 123, 125, 133, 135, 143, 145, 153, 159, 161, 169, 175, 177, 185, 187, 193, 195, 203, 219, 221, 225, 227, 235, 237, 245, 251, 259, 263, 267, 269, 277, 279, 289, 303, 305, 309, 311, 325, 333, 341, 345, 349, 353, 363, 369, 375, 379, 385, 393

Offset: 1

Author

N. J. A. Sloane, May 03 2022

Keywords

• nonn

Comments

Note this is different from "a(n) = index of prime(n) in A093714", which would start 3, 2, 4, 6, 8, ..., but would otherwise be the same.

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A093714.

Programs

Mathematica

nn = 400; c[] = False; c[1] = True; j = 1; u = 2; Reap[Do[k = u; While[Nand[! TrueQ@ c[k], CoprimeQ[j, k], k != j + 1], k++]; Set[{j, c[k]}, {k, True}]; If[PrimeQ@ k, Sow[i]]; If[k == u, While[TrueQ@ c[u], u++]], {i, 2, nn}]][[-1, -1]] (* _Michael De Vlieger, May 03 2022 *)

Python

from math import gcd
from sympy import isprime
from itertools import count, islice
def agen(): # generator of terms
    an, aset, mink = 1, {1}, 2
    for n in count(1):
        if isprime(an): yield n
        k = mink
        while k in aset or gcd(an, k) != 1 or k-an == 1: k += 1
        an = k
        aset.add(an)
        while mink in aset: mink += 1
print(list(islice(agen(), 78))) # Michael S. Branicky, May 03 2022