Imprint established by Alfred A. Knopf in 1954 to publish quality paperback books. The paperbacks were released as part of the K-Series (K-1 to K-104; K-105 to K-109 were solicited for Fall 1960 but published instead as V-105 to V-109), which ran from 1954-1960. The Vintage line was acquired by Random House on April 17, 1960,* after which most titles were renumbered as part of the V-Series, which continued to V-999, at least.
I found an ad in The Reporter (Google Books has it as vol. 22, p. 10, 1960?) that lists “June Vintage Titles” and has the following solicited titles:
H.L. Mencken on Politics as K-101
The Jacksonian Persuasion (Meyers) as K-102
Domestic Manners of the Americans (Mrs. Trollope) as K-103
Beyond the Mexique Bay (Huxley) as K-104
K-101 through K-104 were definitely published (I have images of the covers of K-101, K-102, & K-104). Vintage titles from 1960 list K-series titles from K-102 to K-109, with K-105 to K-109 having [(Fall 1960)] after their titles. See photo of listing from R-1001a.
Best-Sellers sheds more light. K-101, K-102, K-103, & K-104 are solicited in the July 1, 1960, issue (p. 138), but October 1, 1960, issue, lists V-105, V-106, V-107, V-108, & V-109. Likely that K-101 to K-104 were published prior to the Random House sale and V-105 onward were published after the sale.
Some multi-volume K-Series titles had letter suffixes (e.g., K-53A, K-53B, etc.) -- after the sale to Random House, these multi-volume titles appear to have been given numbers from V-110 to V-123 instead of where they formerly were in the K-Series. This was presumably to remove the letter suffixes.
These are the multi-volume Vintage paperbacks:
K-5A & K-5B (Democracy in America) → V-110 & V-111
K-33A & K-33B (Gide -- The Journals) → V-112 & V-113
K-53A, K-53B, K-53C, & K-53D (The Social History of Art) → V-114, V-115, V-116, & V-117
K-65A & K-65B (Great Operas) → V-118 & V-119
K-68A & K-68B (Great Issues in American History) → V-120 & V-121
K-97A & K-97B (Modern French Painters) → V-122 & V-123
After Random House purchase in 1960, Modern Library paperbacks were reprinted in Vintage V-series. Most of the Modern Library paperbacks were assigned V-Series numbers after the old multi-volume sets, from V-124 to V-173. One Modern Library Paperback (P6b -- The Sound and the Fury) was assigned V-5 in place of K-5A & K-5B (the two volumes of de Tocqueville), which were reassigned to V-110 & V-111. Two others (P28 & P32) were given series numbers previously used by books not carried over to the V-Series: V-18 & V-49.
For clarity, see Vintage Books Absorbing Modern Library Paperbacks, PW, July 18, 1960, at 46 (explaining the new combined series will use V-numbers and specifying the change will start with new five Vintage Books published in September and six Vintage Russian Library and nine Modern Library Paperbacks titled issued in August and September).
V-501 through V-530 (?) formed a sub-series named Caravelle Editions. These titles were issued in a larger format.
Paperbound Books for Colleges (Random House 196?)
* Margaret Becket, Random House, in AMERICAN LITERARY PUBLISHING HOUSES, 1900-1980: TRADE AND PAPERBACK, 46 DICTIONARY OF LITERARY BIOGRAPHY 307 (1986) (“On 17 April 1960 Random House acquired Alfred A. Knopf, Incorporated, with Knopf and his wife Blanche retaining editorial control of books published under their respected Borzoi imprint. Acquired with Knopf was the Vintage line of quality paperbacks.”)