A389084 Primegap shift: fully multiplicative with a(prime(j)) = A130789(1+A389083(j)).

1, 5, 7, 25, 13, 35, 2, 125, 49, 65, 47, 175, 23, 10, 91, 625, 53, 245, 31, 325, 14, 235, 19, 875, 169, 115, 343, 50, 199, 455, 11, 3125, 329, 265, 26, 1225, 61, 155, 161, 1625, 293, 70, 89, 1175, 637, 95, 113, 4375, 4, 845, 371, 575, 37, 1715, 611, 250, 217, 995, 127, 2275, 43, 55, 98, 15625, 299, 1645, 211, 1325

Offset

1,2

Comments

Here each prime in A130789 is mapped to the next prime in that sequence, as 3 -> 7 -> 2 -> 5 -> 13 -> 23 -> 19 -> 31 -> 11 -> 47 -> ..., and the other values are determined by the multiplicativity.

Links

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

Index entries for primes, gaps between.

Prog

(PARI)
v130789 = readvec("b130789_to.txt"); \\ Prepared with gawk ' { print $2 } ' < b130789.txt > b130789_to.txt
A130789(n) = v130789[n];
invmap = Map(); for(i=1, #v130789, mapput(invmap, primepi(A130789(i)), i));
A389083(n) = mapget(invmap, n);
A389084(n) = { my(f=factor(n)); f[, 1] = apply(p->A130789(1+A389083(primepi(p))), f[, 1]); factorback(f); };

Crossrefs

Cf. A130789, A389083, A389085 (left inverse), A389086 (primeshift array).

Permutation of non-multiples of 3, A001651.

Sequence in context: A298900 A357852 A166660 * A354202 A037374 A056717

Adjacent sequences: A389081 A389082 A389083 * A389085 A389086 A389087

Keyword

nonn,mult

Author

Antti Karttunen, Sep 24 2025

Status

approved