A302850 Permutation of natural numbers: a(1) = 1; a(2) = 2; for n > 2, a(n) = 2+A064989(A003961(n)-4).

1, 2, 3, 5, 4, 9, 7, 21, 12, 15, 6, 39, 13, 25, 31, 37, 8, 69, 19, 55, 28, 17, 11, 129, 14, 45, 51, 53, 10, 99, 16, 235, 61, 49, 73, 145, 33, 35, 18, 95, 24, 97, 43, 111, 70, 81, 27, 399, 46, 79, 57, 141, 23, 237, 48, 285, 64, 85, 36, 309, 22, 105, 271, 209, 59, 183, 63, 165, 88, 225, 40, 415, 20, 67, 241, 117, 139, 243, 75, 559, 154, 29, 41, 489, 84, 133

Offset: 1

Author

Antti Karttunen, Apr 26 2018

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Index entries for sequences that are permutations of the natural numbers
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A302849 (inverse).

Cf. A003961, A064989, A302848.

Programs

PARI

A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
A302850(n) = if(n<=2,n,2+A064989(A003961(n)-4));

Formula

a(1) = 1; a(2) = 2; for n > 2, a(n) = 2+A064989(A003961(n)-4).