A302847 Permutation of natural numbers: a(1) = 1; for n > 1, a(n) = A064989(2+A003961(n-1)).

1, 2, 3, 5, 7, 4, 13, 11, 23, 8, 19, 6, 43, 17, 15, 31, 79, 10, 35, 9, 33, 34, 37, 29, 131, 26, 47, 113, 97, 14, 103, 22, 75, 61, 53, 73, 223, 41, 67, 46, 181, 12, 163, 25, 65, 106, 83, 21, 217, 74, 139, 89, 87, 59, 253, 58, 209, 44, 51, 20, 313, 38, 109, 271, 533, 49, 193, 71, 167, 50, 229, 18, 673, 16, 27, 187, 119, 69, 251, 39, 563, 238, 127, 55, 335, 24

Offset: 1

Author

Antti Karttunen, Apr 26 2018

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• David Newman, et al., New sequences from old, Discussion on SeqFan-mailing list, January 2018.
• Index entries for sequences that are permutations of the natural numbers
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A302848 (inverse).

Cf. A003961, A048673, A064216, A064989.

Cf. also A297165, A302849.

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)};
A302847(n) = if(1==n,n,A064989(2+A003961(n-1)));

Formula

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

a(1) = 1; for n > 1, a(n) = A064216(1+A048673(n-1)).