A305294 -id:A305294 - cp's OEIS frontend

A305293 Prime shift towards larger primes, conjugated by the EKG-permutation: a(n) = A064664(A003961(A064413(n))).

1, 5, 6, 11, 10, 24, 39, 22, 15, 14, 25, 69, 21, 20, 53, 130, 76, 51, 29, 28, 54, 112, 97, 50, 78, 96, 34, 33, 84, 209, 232, 38, 37, 85, 153, 44, 43, 111, 156, 179, 109, 58, 57, 142, 383, 140, 148, 352, 281, 124, 249, 299, 93, 118, 218, 62, 61, 143, 172, 68, 67, 173, 641, 696, 162, 75, 74, 210, 227, 238, 191, 535, 82, 81

Offset: 1

Antti Karttunen, May 31 2018

nonn

Permutation of A064957.

Cf. A305294 (a left inverse).

Cf. A003961, A064413, A064423, A064664, A064955, A064957.

a(n) = A064664(A003961(A064413(n))).
Other identities. For all n >= 1:
A305294(a(n)) = n.
a(A064955(n)) = A064955(1+n).
For all n >= 2, a(A064423(n)) = 1+A064955(1+n).

A318664 Numerators of the sequence whose Dirichlet convolution with itself yields A064664, the inverse permutation of EKG-sequence.

Original entry on oeis.org

1, 1, 5, 1, 5, -1, 7, 3, -1, -1, 10, 3, 14, -1, -7, 5, 33, 59, 37, 9, -10, -1, 43, -1, -1, -1, 181, 13, 57, 89, 61, 15, -29, -1, -45, 31, 67, -1, -41, 1, 37, 129, 81, 11, 301, -1, 89, 21, 1, 26, -97, 10, 50, -93, -47, -5, -109, -1, 107, -33, 115, -1, 411, 15, -43, 201, 64, 33, -127, 56, 67, 181, 69, -1, 283, 35, -31, 255, 151, 7

Offset: 1

Antti Karttunen, Sep 01 2018

Antti Karttunen, Table of n, a(n) for n = 1..16384
Index entries for sequences related to EKG sequence

Cf. A064664, A304526, A304527, A305293, A305294, A318665 (denominators).

Cf. also A317929, A317930.

v064413 = readvec("b064413_upto65539_terms_only.txt"); \\ From b-file of A064413 prepared beforehand.
A064413(n) = v064413[n];
m064664 = Map();
for(n=1,65539,mapput(m064664,A064413(n),n));
A064664(n) = mapget(m064664,n);
up_to = (2^14);
DirSqrt(v) = {my(n=#v, u=vector(n)); u[1]=1; for(n=2, n, u[n]=(v[n]/v[1] - sumdiv(n, d, if(d>1&&dA317937.
v318664_65 = DirSqrt(vector(up_to, n, A064664(n)));
A318664(n) = numerator(v318664_65[n]);
A318665(n) = denominator(v318664_65[n]);

a(n) = numerator of f(n), where f(1) = 1, f(n) = (1/2) * (A064664(n) - Sum_{d|n, d>1, d 1.

For n >= 2, a(2*A000040(n)) = -1.

cp's OEIS Frontend

A305293 Prime shift towards larger primes, conjugated by the EKG-permutation: a(n) = A064664(A003961(A064413(n))).

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