Binomial-Coefficient Selfie Numbers Generator

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From

Digit order Original orderabc → a, b, c Reverse orderabc → c, b, a Both ordersSearch abc → a, b, c and abc → c, b, a.

Binomial-Coefficient Binomial B(n,r)Show only B(n,r) representations; selected √ and ! operations may appear inside its arguments.

Maximum B depth

Optional operations inside the chosen representation Basic operations + powersUsed to build the arguments of the selected function: +, −, ×, ÷ and a^b. Multiple square rootsAllow square roots within a representation using the selected function. Multiple factorialsAllow factorials within a representation using the selected function.

Maximum √ depth

Maximum ! depth

Solutions for each number and digit order Single solutionShow one representation per number and digit order. Faster search. Multiple solutionsSearch for distinct representations, including different function and optional-operation combinations.

Maximum solutions per number and digit order

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Intermediate limit

Exact integer division is used. The intermediate limit prevents powers and repeated factorials from exhausting the browser.

Verified output

Selfie representations

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Choose an interval and operations, then generate. Results will appear here as they are verified.

References

This work is based on the author’s following research:

Inder J. Taneja, Selfie Numbers with Binomial Coefficients, Zenodo, March 17, 2019, pp. 1–131. doi:10.5281/zenodo.2596421 ↗

Inder J. Taneja, Selfie Numbers with Binomial Coefficients and Fibonacci Numbers, Zenodo, March 30, 2019, pp. 1–148. doi:10.5281/zenodo.2617290 ↗

Inder J. Taneja, Binomial Coefficients Triangular Type Selfie Numbers: Basic Operations, Zenodo, April 25, 2019, pp. 1–72. doi:10.5281/zenodo.2650508 ↗

Inder J. Taneja, Selfie Numbers with Binomial Coefficients, Triangular Numbers and Square-Root, Zenodo, May 10, 2019, pp. 1–209. doi:10.5281/zenodo.2707318 ↗

Inder J. Taneja, Selfie Numbers with Binomial Coefficients, Triangular Numbers and Factorial, Zenodo, July 9, 2019, pp. 1–172. doi:10.5281/zenodo.3273300 ↗

Previous work:

Inder J. Taneja, Selfie Numbers and Binomial Coefficients, RGMIA Research Report Collection, 20 (2017), Art. 25, pp. 1–18. RGMIA PDF ↗

Inder J. Taneja, Binomial Coefficients Type Selfie Numbers, RGMIA Research Report Collection, 21 (2018), Art. 102, pp. 1–113. RGMIA PDF ↗

Inder J. Taneja, Binomial Coefficient Type Selfie Numbers: Digit’s Order, September 25, 2018. WordPress article ↗

Inder J. Taneja, Binomial Coefficient Type Selfie Numbers: Reverse Order of Digits, September 25, 2018. WordPress article ↗

Inder J. Taneja, Selfie Numbers and Binomial Coefficients, October 28, 2017. WordPress article ↗