A181709 -id:A181709 - cp's OEIS frontend

A236866 Positions of primes in A007775 (numbers not divisible by 2, 3 or 5).

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 22, 23, 24, 26, 27, 28, 29, 30, 31, 34, 35, 37, 38, 40, 41, 42, 44, 45, 47, 48, 49, 51, 52, 53, 54, 57, 60, 61, 62, 63, 64, 65, 67, 69, 71, 72, 73, 74, 75, 76, 79, 82, 83, 84, 85, 89, 90, 93, 94, 95

Offset: 1

Alex Ratushnyak, Jan 31 2014

From Antti Karttunen, Feb 01 2014: (Start)
Positions of primes among natural numbers coprime to 30.
Term 1 is missing from the sequence, because A007775(1)=1 is not considered a prime, terms 2 - 13 are all present, and 14 is the next term missing from here, as A007775(14)=49 is the first composite in that sequence.
(End)

Antti Karttunen, Table of n, a(n) for n = 1..10000

Cf. A007775, A181709.

from sympy import isprime
i=0
for n in range(1000):
    if n%2 and n%3 and n%5:
        i+=1   # A007775(i)=n
        if isprime(n):  print(i, end=', ')

;; With Antti Karttunen's IntSeq-library.
(define A236866 (MATCHING-POS 1 1 (lambda (n) (prime? (A007775 n)))))
;; Where a slow version of A007775 can be defined for example like this,
(define A007775 (MATCHING-POS 1 1 (lambda (n) (= 1 (gcd n 30)))))
;; from Antti Karttunen, Feb 01 2014

A334495 Position of prime(n) in A045572, a(1) = a(3) = 0.

Original entry on oeis.org

0, 2, 0, 3, 5, 6, 7, 8, 10, 12, 13, 15, 17, 18, 19, 22, 24, 25, 27, 29, 30, 32, 34, 36, 39, 41, 42, 43, 44, 46, 51, 53, 55, 56, 60, 61, 63, 66, 67, 70, 72, 73, 77, 78, 79, 80, 85, 90, 91, 92, 94, 96, 97, 101, 103, 106, 108, 109, 111, 113, 114, 118, 123, 125, 126

Offset: 1

Michael De Vlieger, Aug 27 2020

A045572 contains the positive numbers coprime to 10.

Nondivisor primes p (i.e., all primes except p | 10, that is, 2 or 5) belong to one of four residues r (i.e., 1, 3, 7, 9) in the reduced residue system mod 10. Therefore all primes aside from 2 and 5 appear in A045572. On account of this fact, one may use A045572 as a sort of prime sieve. This use is less efficient than searching for primes aside from 2 and 3 amid numbers that are +/-1 (mod 6), i.e., in A007310, and slightly more efficient than searching for primes aside from 2 amid the odd numbers, but in line with the common (decimal) base.

			a(1) = a(3) = 0 by definition, since 2 and 5 are not in A045572.
a(2) = 2 since A045572(2) = 3, a(10) = 12 since prime(10) = 29 = A045572(12), etc.

Cf. A000040, A045572. Analogous to A181709.

Array[If[FreeQ[{2, 5}, #], 4 #1 + (#2 + 1)/2 - Boole[#2 > 5] & @@ QuotientRemainder[#, 10], 0] &@ Prime@ # &, 65]

For prime p_n for n =/= 1 nor n =/= 3, a(p_n) = 4*q + (r + 1)/2 - [r > 5] (Iverson brackets), where q = floor(p_n/10) and r = p_n mod 10.

cp's OEIS Frontend

A236866 Positions of primes in A007775 (numbers not divisible by 2, 3 or 5).

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