A257950 Numbers n which are both happy (A007770) and bihappy (A257795) numbers.

1, 10, 100, 103, 301, 367, 608, 806, 1000, 1030, 3010, 3056, 5630, 6080, 6703, 6791, 8060, 9167, 10000, 10003, 10275, 10300, 11241, 12770, 12939, 13929, 14112, 17027, 17502, 20175, 21921, 22119, 27501, 30001, 30067, 30100, 30616, 31606, 36700

Offset

1,2

Comments

This sequence is infinite, because it contains infinite subsequences (powers of 10, for example).

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000

Formula

All 10^k are members of this sequence.

If n is a member each permutation of a set of pairs of digits gives another members (example 367 and 6703).

Placing two zeros between the sets of two digits gives another member.

Example

367 is member of this sequence because 367 = 3^2+6^2+7^2= 94 => 9^2+4^2 = 97 => 9^2+7^2 = 130 => 1^2+3^2+0^2 = 10 => 1^2+0^2 = 1, so after five iterations 367 reaches 1. And 3^2+67^2 = 4498 => 44^2+98^2= 11540 => 1^2+15^2+40^2 = 1826 => 18^2+26^2 = 1000 => 10^2+0^2 = 100 =>1^2+0^2 = 1, so in 6 iterations 367 reaches 1.

Crossrefs

Cf. A007770, A257795.

Sequence in context: A342135 A169665 A257795 * A052009 A355592 A357300

Adjacent sequences: A257947 A257948 A257949 * A257951 A257952 A257953

Keyword

nonn,base

Author

Pieter Post, May 14 2015

Status

approved