Can anyone out there help me with this. I need to find the next number in the sequence below. It is a proper sequence, in that there is a rule to generate the next element. If I can find the rule, there maybe a considerable reward. It is part of a larger problem, but I think that if I can crack this part, I have the rest. 1,2,5,7,12,15,22,35,40,57,70,77,92

Hi Cremeegg, This has me foxed. I thought I had it cracked - as a generalised pentagonal number sequence as per the attached link: https://en.wikipedia.org/wiki/Pentagonal_number All the numbers mentioned above fall into this sequence - it's just that there should be additional numbers also. Ouch!

Thats brilliant Dan, I some have further numbers in the sequence and I checked the first 33 generalised pentagonal numbers map the first 22 numbers of my sequence, with none missed. The previous system I was using produced 392 numbers to give me the first 22 numbers. The prize is simply for finding the next number, generating 3 or more and testing to find the correct one may not be pretty but I think it is acceptable. Of course a formula to generate the sequence and only the sequence would be ideal.

Last edited by a moderator: Jan 6, 2018 Happy that it may help! Now let's deal with the elephant in the room or, as some might put it, the moral issue here. What's my percentage?! Regarding the quote above, my gut tells me it's impossible - but I'm just after reading Thinking Fast and Slow and think I'll never be able to trust my gut again!! [Me writing the immediate above is good news for you - there are some smart buachaillí out there who would just love to demonstrate how unreliable my gut is!!]

Indeed. The type of thinking deficits that he discusses can, on occasion, make appearances in these here parts - including by yours truly, not more than most, but occasionally nonetheless!

I think it is fair to say that the Kudos from solving this would quieten those buachaillí or indeed Cailiní for a while. Speaking of whom, where has your friend the Duke gone.

I just don't know. He just said he wasn't going to engage with me anymore - unilaterally breaking off our engagement. If I'm totally honest, I think it had been coming for some time. Still, it's disappointing.