# Tag Archives: Pentagonal number

## Num3er 1258723

A Pentagonal number is a polygonal number of the form     is a prime number.     is also prime index of a 13-digital palindromic pentagonal number                     … Continue reading

## Triangular numbers which are the sum of 3 pentagonal numbers

Pentagonal numbers:       Let     represent the n-th triangular number and     the n-th pentagonal number For any integer   ,   if   ,   then the sum    equals      since … Continue reading

## Primitive Pythagorean triples with the odd leg a Pentagonal number

There are infinitely many primitive Pythagorean triples   ,   like   , with hypotenuse c such that the odd leg is a pentagonalnumber and the even leg is consecutive with the hypotenuse. The odd leg a being … Continue reading

## Octagonal number and its complementary Pentagonal number

An integer of the form     is called a Pentagonal number An integer of the form     is called an Octagonal number   if   then     and     are said to be complements of … Continue reading

## Pentagonals (P(2), P(A), P(B)) in arithmetic progression

If   ,    then       c. d. is the common difference           c. d.   =     c. d. =     c. d. =     c. d. =   … Continue reading

## Pentagonals (P(1), P(A), P(B)) in arithmetic progression

If   ,    then   Here are the first few solutions:       =   common difference

## The smallest pairs of triangular & pentagonal numbers

Find the smallest pair of …     (1) … triangular numbers whose sum and difference is triangular     (2) … pentagonal numbers whose sum and difference is pentagonal                 … Continue reading

## Harmonic mean between two consecutive triangular numbers is Pentagonal

An integer of the form     is called a Triangular number.   An integer of the form     is called a Pentagonal number.   To find     such that the Harmonic mean between two consecutive … Continue reading

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## Difference between an Oblong number and Pentagonal is 1

Oblong numbers are of the form ,     where     is the n-th triangular number.   An integer of the form     is called a Pentagonal number.   The first few solutions are :       … Continue reading