A024702 -id:A024702 - cp's OEIS frontend

A024707 Positions of multiples of 5 in A024702.

5, 8, 10, 11, 13, 17, 18, 20, 22, 24, 26, 29, 32, 34, 35, 36, 41, 42, 43, 46, 47, 50, 52, 53, 54, 57, 58, 60, 64, 67, 70, 72, 75, 77, 79, 80, 81, 82, 83, 85, 87, 89, 92, 94, 95, 97, 98, 100, 104, 105, 109, 110, 114, 115, 116, 120, 121, 125, 126, 127, 128, 131, 133, 135, 136, 140, 141

Offset: 1

Clark Kimberling

nonn

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A244738, A244739, A244741.

A024707:=n->`if`((ithprime(n) mod 5) mod 3 = 1, n, NULL): seq(A024707(n), n=1..150); # Wesley Ivan Hurt, Jul 06 2014

z = 300; u = Mod[Table[Mod[Prime[n], 5], {n, 1, z}], 3] (* A244738 *)
v1 = Flatten[Position[u, 0]]  (* A244739 *)
v2 = Flatten[Position[u, 1]]  (* A024707 *)
v3 = Flatten[Position[u, 2]]  (* A244741 *) (* Clark Kimberling , Jul 05 2014 *)

apply(n->primepi(n), select(n->n%9==1||n%9==8, primes(100))) \\ Charles R Greathouse IV, May 31 2013

Numbers n such that ((prime(n) mod 5) mod 3) = 1; e.g., prime(10) = 29, (29 mod 5) = 4, and (4 mod 3) = 1. Clark Kimberling, Jul 05 2014

A024704 Positions of even numbers in A024702.

Original entry on oeis.org

4, 7, 9, 11, 13, 15, 20, 21, 22, 24, 25, 27, 30, 31, 33, 36, 39, 43, 44, 46, 48, 51, 52, 53, 55, 56, 58, 60, 64, 65, 68, 71, 72, 73, 76, 79, 80, 83, 84, 85, 87, 88, 90, 92, 93, 96, 98, 104, 106, 108, 109, 110, 111, 113, 115, 116, 118, 122, 128, 129, 132, 133, 135, 136, 140, 143, 146

Offset: 1

Clark Kimberling

Indices of primes which are 1 or 7 mod 8. - Charles R Greathouse IV, May 30 2013

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

apply(n->primepi(n),select(n->n%8==1||n%8==7,primes(100))) \\ Charles R Greathouse IV, May 30 2013

Adjusted for offset. - Charles R Greathouse IV, May 30 2013

A024705 Positions of odd numbers in A024702.

Original entry on oeis.org

3, 5, 6, 8, 10, 12, 14, 16, 17, 18, 19, 23, 26, 28, 29, 32, 34, 35, 37, 38, 40, 41, 42, 45, 47, 49, 50, 54, 57, 59, 61, 62, 63, 66, 67, 69, 70, 74, 75, 77, 78, 81, 82, 86, 89, 91, 94, 95, 97, 99, 100, 101, 102, 103, 105, 107, 112, 114, 117, 119, 120, 121, 123, 124, 125, 126, 127, 130, 131, 134

Offset: 1

Clark Kimberling

Indices of primes > 3 which are 3 or 5 mod 8. - Charles R Greathouse IV, May 30 2013

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Flatten[Position[Table[If[MemberQ[{3,5},Mod[n,8]],1,0],{n,Prime[ Range[ 3,200]]}],1]]+2 (* Harvey P. Dale, May 26 2018 *)

apply(n->primepi(n),select(n->n%8==3||n%8==5,primes(100))) \\ Charles R Greathouse IV, May 30 2013

Adjusted for offset. - Charles R Greathouse IV, May 30 2013

A024710 Greatest prime divisor of A024702(n).

Original entry on oeis.org

2, 5, 7, 3, 5, 11, 7, 5, 19, 7, 11, 23, 13, 29, 31, 17, 7, 37, 13, 41, 11, 7, 17, 17, 53, 11, 19, 7, 13, 23, 23, 37, 19, 79, 41, 83, 43, 89, 13, 19, 97, 11, 11, 53, 37, 113, 23, 29, 17, 11, 7, 43, 131, 67, 17, 139, 47, 71, 73, 17, 31, 157, 79, 83, 13, 173, 29, 59, 179, 61, 31, 19, 191, 97

Offset: 4

Clark Kimberling

nonn

Charles R Greathouse IV, Table of n, a(n) for n = 4..10000

a(n)=my(f=factor(prime(n)^2\24)[,1]);f[#f] \\ Charles R Greathouse IV, May 30 2013

A024703 Prime divisors, including repetitions, of n-th term of A024702.

Original entry on oeis.org

0, 1, 1, 1, 3, 2, 2, 2, 4, 2, 3, 2, 3, 3, 2, 2, 2, 4, 3, 4, 2, 4, 5, 3, 3, 3, 4, 4, 7, 3, 3, 3, 3, 4, 2, 4, 3, 2, 3, 4, 6, 5, 4, 5, 3, 5, 2, 3, 4, 5, 5, 5, 7, 3, 4, 6, 2, 4, 2, 3, 4, 4, 3, 2, 3, 5, 2, 4, 5, 4, 4, 3, 5, 6, 3, 3, 5, 4, 4, 3, 6, 6, 4, 3, 8, 3, 4, 5, 3, 5, 6, 4, 4, 4, 3, 5, 3, 4, 3, 3, 2, 4, 4, 7, 3, 6, 5, 5, 5, 3, 4

Offset: 3

Clark Kimberling

nonn

Charles R Greathouse IV, Table of n, a(n) for n = 3..10000

a(n)=bigomega(prime(n)^2\24) \\ Charles R Greathouse IV, May 30 2013

A024706 Positions of multiples of 3 in A024702.

Original entry on oeis.org

7, 8, 12, 16, 20, 21, 24, 28, 29, 31, 38, 41, 42, 45, 46, 51, 54, 57, 58, 63, 72, 75, 78, 83, 84, 87, 91, 93, 96, 98, 99, 100, 102, 106, 108, 112, 115, 118, 124, 126, 128, 131, 134, 137, 140, 141, 144, 145, 150, 152, 153, 157, 159, 162, 164, 167, 169, 178, 179, 184, 187, 190, 191

Offset: 1

Clark Kimberling

nonn

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

apply(n->primepi(n), select(n->n%9==1||n%9==8, primes(100))) \\ Charles R Greathouse IV, May 31 2013

Adjusted for offset. - Charles R Greathouse IV, May 31 2013

A024708 Number of distinct prime divisors of n-th term of A024702.

Original entry on oeis.org

0, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 4, 3, 3, 2, 4, 2, 2, 3, 2, 3, 3, 3, 3, 3, 3, 2, 3, 2, 2, 3, 2, 3, 4, 3, 2, 3, 4, 3, 3, 2, 3, 4, 4, 3, 3, 2, 3, 3, 4, 2, 4, 2, 2, 4, 4, 3, 2, 3, 3, 2, 3, 3, 4, 3, 3, 4, 2, 3, 3, 3, 4, 4, 3, 4, 4, 4, 3, 4, 3, 4, 4, 3, 3, 3, 3, 2, 4, 3, 5, 3, 3, 3, 3

Offset: 3

Clark Kimberling

nonn

Charles R Greathouse IV, Table of n, a(n) for n = 3..10000

[#PrimeDivisors(NthPrime(n)^2 div 24): n in [3..100]]; // Vincenzo Librandi, Apr 27 2019

PrimeNu[(Prime[Range[3, 100]]^2 - 1) / 24] (* Vincenzo Librandi, Apr 27 2019 *)

a(n)=omega(prime(n)^2\24) \\ Charles R Greathouse IV, May 30 2013

a(25) and other terms corrected by Charles R Greathouse IV, May 30 2013

A024709 Least prime divisor of A024702(n).

Original entry on oeis.org

2, 5, 7, 2, 3, 2, 5, 2, 3, 2, 7, 2, 3, 5, 5, 11, 2, 2, 2, 7, 2, 2, 5, 2, 3, 3, 2, 2, 5, 2, 5, 5, 2, 13, 3, 2, 29, 3, 3, 2, 2, 3, 2, 5, 2, 19, 5, 2, 2, 2, 3, 2, 2, 3, 2, 23, 2, 47, 7, 3, 2, 2, 53, 5, 2, 29, 5, 2, 2, 2, 11, 3, 2, 5, 3, 2, 2, 5, 5, 2, 2, 2, 13, 2, 2, 5, 2, 3, 2, 2, 5, 5, 2, 5, 2, 3, 3, 7, 3, 47, 2, 5, 2, 7, 2, 2

Offset: 4

Clark Kimberling

nonn

Charles R Greathouse IV, Table of n, a(n) for n = 4..10000

Cf. A020639, A024702.

a(n)=factor(prime(n)^2\24)[1,1] \\ Charles R Greathouse IV, May 30 2013

a(n) = A020639(A024702(n)). - Michel Marcus, Sep 24 2023

A024711 a(n) = residue mod 2 of n-th term of A024702.

Original entry on oeis.org

1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0

Offset: 3

Clark Kimberling

Charles R Greathouse IV, Table of n, a(n) for n = 3..10000

a(n)=my(p=prime(n)%8);p==3||p==5 \\ Charles R Greathouse IV, May 31 2013

A024712 a(n) = residue mod 3 of n-th term of A024702.

Original entry on oeis.org

1, 2, 2, 1, 0, 0, 1, 2, 1, 0, 1, 2, 2, 0, 1, 2, 1, 0, 0, 2, 2, 0, 2, 2, 1, 0, 0, 1, 0, 1, 2, 1, 1, 2, 1, 0, 1, 2, 0, 0, 2, 1, 0, 0, 1, 2, 2, 1, 0, 1, 2, 0, 1, 2, 0, 0, 2, 2, 1, 1, 0, 1, 2, 2, 2, 1, 1, 2, 2, 0, 2, 1, 0, 1, 2, 0, 1, 1, 1, 2, 0, 0, 2, 2, 0, 2, 2, 1, 0, 2, 0, 1, 1, 0, 1, 0, 0, 0, 2, 0, 1, 2, 1, 0, 2, 0, 1, 2, 1, 0, 1

Offset: 3

Clark Kimberling

nonn

Charles R Greathouse IV, Table of n, a(n) for n = 3..10000

a(n)=prime(n)^2\24%3 \\ Charles R Greathouse IV, May 31 2013

cp's OEIS Frontend

A024707 Positions of multiples of 5 in A024702.

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Maple

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A024704 Positions of even numbers in A024702.

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A024705 Positions of odd numbers in A024702.

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A024710 Greatest prime divisor of A024702(n).

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A024703 Prime divisors, including repetitions, of n-th term of A024702.

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A024706 Positions of multiples of 3 in A024702.

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PARI

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A024708 Number of distinct prime divisors of n-th term of A024702.

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Magma

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A024709 Least prime divisor of A024702(n).

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A024711 a(n) = residue mod 2 of n-th term of A024702.

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PARI

A024712 a(n) = residue mod 3 of n-th term of A024702.