A354092 Fully multiplicative prime shift where the primes of the form 3k+2 are replaced by the previous such prime (with 2 -> 1), and primes of the form 3k and 3k+1 stay as they are.

1, 1, 3, 1, 2, 3, 7, 1, 9, 2, 5, 3, 13, 7, 6, 1, 11, 9, 19, 2, 21, 5, 17, 3, 4, 13, 27, 7, 23, 6, 31, 1, 15, 11, 14, 9, 37, 19, 39, 2, 29, 21, 43, 5, 18, 17, 41, 3, 49, 4, 33, 13, 47, 27, 10, 7, 57, 23, 53, 6, 61, 31, 63, 1, 26, 15, 67, 11, 51, 14, 59, 9, 73, 37, 12, 19, 35, 39, 79, 2, 81, 29, 71, 21, 22, 43, 69, 5, 83

Offset

1,3

Links

Table of n, a(n) for n=1..89.

Index entries for sequences computed from indices in prime factorization

Formula

Fully multiplicative with a(2) = 1, a(A003627(1+n)) = A003627(n), a(A007645(n)) = A007645(n).

For all n >= 1, a(A354091(n)) = n.

Prog

(PARI) A354092(n) = { my(f=factor(n)); for(k=1, #f~, if(2==(f[k, 1]%3), if(2==f[k, 1], f[k, 1]--, forstep(i=primepi(f[k, 1])-1, 0, -1, if(2==(prime(i)%3), f[k, 1]=prime(i); break))))); factorback(f); };

Crossrefs

Left inverse of A354091.

Cf. A003627, A007645.

Cf. A064989, A348747 (variants).

Sequence in context: A345037 A175945 A209859 * A262218 A362940 A331695

Adjacent sequences: A354089 A354090 A354091 * A354093 A354094 A354095

Keyword

nonn,mult

Author

Antti Karttunen, May 17 2022

Status

approved