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A323142 Envelope numbers (see the Comments section for the definition). 2
100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 600, 601, 602, 603, 604, 605, 606, 607, 608, 609, 700, 701, 702, 703, 704 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
An envelope number N has two parts E and C such that C is a multiple of E; E is the concatenation of the first and the last digit of N (the Envelope) and C is the concatenation of the other digits (the Content of the envelope). The integer 12348 is a member of the sequence as 234 (the Content) is a multiple of 18 (the Envelope): indeed 234 = 18*13. Contents that have a leading zero are not admitted (10347 is not a regular envelope number though 34 is a multiple of 17).
Note that some envelope numbers might fit into another envelope (and so on): see the Crossrefs section.
This sequence begins with the same 90 terms of A252480 then differs: A252480(91) = 1000 and A323142(91) = 1100
LINKS
EXAMPLE
100 has a Content of 0 which is indeed a multiple of the Envelope 10 (0 = 10*0)
101 has a Content of 0 which is indeed a multiple of the Envelope 11 (0 = 11*0)
102 has a Content of 0 which is indeed a multiple of the Envelope 12 (0 = 12*0)
...
1100 has a Content of 10 which is indeed a multiple of the Envelope 10 (10 = 10*1)
1111 has a Content of 11 which is indeed a multiple of the Envelope 11 (11 = 11*1)
1122 has a Content of 12 which is indeed a multiple of the Envelope 12 (12 = 12*1)
...
1263 has a Content of 26 which is indeed a multiple of the Envelope 13 (26 = 13*2)
MATHEMATICA
Select[Range[100, 704], Or[#1 == 0, Mod[#1, #2] == 0] & @@ {If[And[First@ # == 0, Length@ # > 1], -1, FromDigits@ #] &@ Most@ Rest@ #, FromDigits@ {First@ #, Last@ #}} &@ IntegerDigits@ # &] (* Michael De Vlieger, Jan 07 2019 *)
PROG
(PARI) isok(n, base=10) = my (d=digits(n, base)); #d>=3 && (#d==3 || d[2]) && ((n-d[1]*base^(#d-1))\base) % (d[1]*base+d[#d])==0 \\ Rémy Sigrist, Jan 06 2019
CROSSREFS
Cf. A323143 (envelope numbers that fit into successive bigger envelopes).
Cf. A252480.
Sequence in context: A135641 A330859 A252480 * A220401 A169737 A070794
KEYWORD
base,nonn
AUTHOR
STATUS
approved

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)