# 47

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## Number

$47$ (forty-seven) is:

The $15$th prime number, after $2$, $3$, $5$, $7$, $11$, $13$, $17$, $19$, $23$, $29$, $31$, $37$, $41$, $43$

The $1$st of the largest known pair of Ulam numbers which differ by $1$:
$47 = 11 + 36, \ 48 = 1 + 47$

The $1$st number such that the result when adding $2$ is the reversal of when multiplying by $2$:
$47 + 2 = 49$; $47 \times 2 = 94$

The $4$th and last of the $1$st ordered quadruple of consecutive integers that have sigma values which are strictly decreasing:
$\map \sigma {44} = 84$, $\map \sigma {45} = 78$, $\map \sigma {46} = 72$, $\map \sigma {47} = 48$

The $2$nd integer $m$ after $1$ whose cube can be expressed as the sum of $m$ consecutive squares:
$47^3 = \displaystyle \sum_{k \mathop = 1}^{47} \paren {21 + k}^2$

The $4$th Keith number after $14$, $19$, $28$:
$4, 7, 11, 18, 29, 47, \ldots$

The $4$th Thabit number after $(2)$, $5$, $11$, $23$, and $5$th Thabit prime:
$47 = 3 \times 2^4 - 1$

The $4$th of $29$ primes of the form $2 x^2 + 29$:
$2 \times 3^2 + 29 = 47$ (Previous  ... Next)

The $5$th safe prime after $5$, $7$, $11$, $23$:
$47 = 2 \times 23 + 1$

The $6$th Lucas prime after $2$, $3$, $7$, $11$, $29$

The $6$th long period prime after $7$, $17$, $19$, $23$, $29$

The $7$th prime $p$ after $11$, $23$, $29$, $37$, $41$, $43$ such that the Mersenne number $2^p - 1$ is composite

The $8$th Lucas number after $(2)$, $1$, $3$, $4$, $7$, $11$, $18$, $29$:
$47 = 18 + 29$

The $15$th Ulam number after $1$, $2$, $3$, $4$, $6$, $8$, $11$, $13$, $16$, $18$, $26$, $28$, $36$, $38$:
$47 = 11 + 36$

The $21$st positive integer which is not the sum of $1$ or more distinct squares:
$2$, $3$, $6$, $7$, $8$, $11$, $12$, $15$, $18$, $19$, $22$, $23$, $24$, $27$, $28$, $31$, $32$, $33$, $43$, $44$, $47$, $\ldots$

The $23$rd odd positive integer that cannot be expressed as the sum of exactly $4$ distinct non-zero square numbers all of which are coprime
$1$, $3$, $5$, $7$, $\ldots$, $35$, $37$, $41$, $43$, $45$, $47$, $\ldots$