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Gilda numbers
Given a number  $n9$">  with digits  $d_1d_2\cdots d_k$, let us define a Fibonacci-like sequence where
\[ a(1)=|d_1-d_2-\cdots-d_k|\,,\quad\quad a(2)=d_1+d_2+\cdots+d_k\,, \]
and  $a(i)=a(i-1)+a(i-2)$  for  $i2$">. If the number  $n$  appear in the sequence of the  $a(i)$'s then  $n$  is called Gilda number.

For example, starting with n=152 we have the sequence |1-5-2|=6, 1+5+2=8, then 14, 22, 36, 58, 94, and finally 152.

The first Gilda numbers are 29, 49, 78, 110, 152, 220, 314, 330, 364, 440, 550, 628, 660, 683, 770, 880, 990, 997 more terms

Pictorial representation of remainders (mod 2, 3, ...,11) frequency. For a table of values and more details click here
remainders of Gilda numbers

A graph displaying how many Gilda numbers are multiples of the primes p from 2 to 71. In black the ideal line 1/p.
divisibility of Gilda numbers
Useful links OEIS, Sequence A042947
Gilda numbers can also be... (you may click on names or numbers and on + to get more values)

aban 29 49 78 110 152 220 314 330 364 440 + 770 880 990 997 abundant 78 220 330 364 440 550 660 770 880 990 + 933138 3120796 3363582 14005576 admirable 78 364 3363582 alternating 29 49 78 65676 amenable 29 49 152 220 364 440 628 660 880 997 + 4484776 14005576 18633637 92078232 amicable 220 apocalyptic 220 660 5346 13064 arithmetic 29 49 78 110 220 330 550 660 683 770 + 3606368 3727761 3970547 4848955 binomial 78 220 330 364 990 brilliant 49 c.octagonal 49 Chen 29 683 2207 congruent 29 78 110 152 220 330 440 550 628 660 + 3120796 3242189 3363582 3606368 Cunningham 440 Curzon 29 78 330 30254 977909 cyclic 29 683 997 2207 73805 977909 3242189 3970547 d-powerful 65676 4848955 de Polignac 997 18633637 30571351 deficient 29 49 110 152 314 628 683 997 2207 13064 + 3849154 3970547 4484776 4848955 dig.balanced 49 78 550 628 660 880 990 35422 38006 202196 933138 14005576 Duffinian 49 977909 3242189 3970547 4848955 economical 29 49 683 997 2207 4848955 emirpimes 49 314 3242189 equidigital 29 49 683 997 2207 4848955 esthetic 78 65676 evil 29 78 330 550 660 683 990 5346 35422 38006 + 18633637 30571351 34610158 786119998 gapful 110 220 330 440 550 660 770 880 990 1377313380 good prime 29 happy 49 440 683 5346 38006 3606368 4848955 Harshad 110 152 220 330 364 440 550 660 770 880 + 3606368 1377313380 9142471346 9410385642 hoax 364 660 house 78 iban 110 220 314 440 770 2207 idoneal 78 330 inconsummate 2207 5346 30254 37862 38006 933138 interprime 660 3727761 Jacobsthal 683 junction 35422 18633637 92078232 Lucas 29 2207 lucky 49 997 magnanimous 29 49 110 152 683 metadrome 29 49 78 modest 29 49 Moran 152 30254 nialpdrome 110 220 330 440 550 660 770 880 990 997 O'Halloran 660 oban 29 78 330 550 628 660 683 770 880 990 997 odious 49 110 152 220 314 364 440 628 770 880 + 3849154 4848955 92078232 271953103 pancake 29 panconsummate 78 pandigital 78 990 pentagonal 330 pernicious 49 110 152 220 314 364 440 628 770 880 997 2207 13064 3849154 Perrin 29 plaindrome 29 49 78 power 49 powerful 49 practical 78 220 330 364 440 660 880 990 5346 prim.abundant 78 364 550 3363582 prime 29 683 997 2207 30571351 271953103 pronic 110 Proth 49 pseudoperfect 78 220 330 364 440 550 660 770 880 990 5346 65676 933138 repunit 364 Ruth-Aaron 49 78 self 110 semiprime 49 314 977909 3242189 4848955 sliding 29 110 Sophie Germain 29 683 sphenic 78 110 30254 35422 37862 38006 73805 143662 3363582 3727761 3849154 3970547 square 49 strong prime 29 30571351 super Niven 110 220 330 440 550 660 770 880 990 super-d 35422 3363582 4484776 tau 152 880 4484776 tetrahedral 220 364 tetranacci 29 triangular 78 990 trimorphic 49 truncatable prime 29 683 997 twin 29 uban 29 49 78 unprimeable 628 38006 73805 202196 933138 3606368 untouchable 628 5346 65676 202196 wasteful 78 110 152 220 314 330 364 440 550 628 + 3727761 3849154 3970547 4484776 weak prime 683 997 2207 Zumkeller 78 220 330 364 440 550 660 770 880 990 5346 65676