A Holiday Brain Teaser

From The Sunday Times, 4th August 1957 [link]

The series below is peculiar in that if any two of the numbers are multiplied together and added to unity, the result is a perfect square:

1, 3, 8

Let A[4], be a fourth number in this series. There is a further series with the same characteristic:

8, B[2], 190, B[4]

in which not only is B[1], the same as A[3], but B[2] is also the same as A[4].

What is B[4]?

(Note: zero is excluded)

This is one of the occasional Holiday Brain Teasers published in The Sunday Times prior to the start of numbered Teasers in 1961. A prize of £5 was offered for a solution to the puzzle, and a further prize of £25 for finding A[5] or B[5].

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