41 lines
2.1 KiB
Text
41 lines
2.1 KiB
Text
A '''cyclops number''' is a number with an odd number of digits that has a zero in the center, but nowhere else. They are named so in tribute to the one eyed giants Cyclops from Greek mythology.
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Cyclops numbers can be found in any base. This task strictly is looking for cyclops numbers in base 10.
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There are many different classifications of cyclops numbers with minor differences in characteristics. In an effort to head off a whole series of tasks with tiny variations, we will cover several variants here.
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;Task
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* Find and display here on this page the first 50 '''cyclops numbers''' in base 10 (all of the sub tasks are restricted to base 10).
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* Find and display here on this page the first 50 '''prime cyclops numbers'''. (cyclops numbers that are prime.)
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* Find and display here on this page the first 50 '''blind prime cyclops numbers'''. (prime cyclops numbers that remain prime when "blinded"; the zero is removed from the center.)
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* Find and display here on this page the first 50 '''palindromic prime cyclops numbers'''. (prime cyclops numbers that are palindromes.)
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;Stretch
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* Find and display the first '''cyclops number''' greater than '''ten million''' (10,000,000) and the index (place) in the series where it is found.
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* Find and display the first '''prime cyclops number''' greater than '''ten million''' (10,000,000) and the index (place) in the series where it is found.
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* Find and display the first '''blind prime cyclops number''' greater than '''ten million''' (10,000,000) and the index (place) in the series where it is found.
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* Find and display the first '''palindromic prime cyclops number''' greater than '''ten million''' (10,000,000) and the index (place) in the series where it is found.
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('''Note:''' there '''''are''''' no cyclops numbers between ten million and one hundred million, they need to have an odd number of digits)
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;See also
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*; [[oeis:A134808|OEIS A134808 - Cyclops numbers]]
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*; [[oeis:A134809|OEIS A134809 - Cyclops primes]]
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*; [[oeis:A329737|OEIS A329737 - Cyclops primes that remain prime after being "blinded"]]
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*; [[oeis:A136098|OEIS A136098 - Prime palindromic cyclops numbers]]
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<br>
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