A246851 a(n) = smallest number k such that sigma(k+n) - sigma(k) = k + n, or -1 if no solution exists.

1, 1, 7, 1, 3577, 1, 25, 8, 13, 1, 403668223, 1, 833, 262, 19, 1, 27, 1, 793, 5, 45, 1, 1795, 66, 8, 9, 31, 1, 2005, 1, 309, 32, 261, 4238, 22490141, 1, 21, 40, 43, 1, 399, 1, 1897, 262, 193, 1, 27, 1252907952, 711, 49, 1158765, 1, 271259, 27, 129, 20518072

Offset: 1

Author

Jaroslav Krizek, Sep 05 2014

Keywords

• sign

Comments

a(p-1) = 1 for any prime p.

a(11) > 11*10^8. - Derek Orr, Sep 05 2014

a(35) > 88*10^7. - Derek Orr, Sep 05 2014

a(185), a(385) and a(869) > 10^11. - Hiroaki Yamanouchi, Sep 11 2014

Examples

			Sequence of numbers k < 10^7  such that sigma(k+n) - sigma(k) = k + n for 1 <= n <= 10:
n = 1: 1, 5, 8585, 16119, ... (A067816).
n = 2: 1, 2, 22, 14926, 31048, 69106, 246262, 5860168, ... (A246852).
n = 3: 7, 6285, 4693485, ... (A246853).
n = 4: 1, 4, 26, 122, 146, 458, 746, 3746, 47612, ... (A246854).
n = 5: 3577, 14773, 2843579, ... (A246855).
n = 6: 1, 3, 114, 116058, 340014, ...
n = 7: 25, 65017, ...
n = 8: 8, 34, 76, 13474, 19042, ...
n = 9: 13, 1743, 1773, 4323, 53175, 109035, 138535, ...
n = 10: 1, 20, 1958, 35150, 49010, 246686, 1030046, 1240694, ...
		

Links

• Hiroaki Yamanouchi, Table of n, a(n) for n = 1..184

Crossrefs

Cf. A000203, A067816, A246852, A246853, A246854, A246855.

Programs

Magma

A246851:=func; [A246851(n): n in[1..100]]

Extensions

a(11)-a(56) from Hiroaki Yamanouchi, Sep 11 2014