A242384 Lesser of consecutive primes whose sum is of the form k*(k+2), for some integer k.
3, 11, 59, 139, 179, 311, 419, 541, 919, 1399, 1621, 2111, 3119, 5099, 6379, 8059, 8839, 9377, 15661, 16007, 16741, 17107, 21011, 21839, 23539, 24419, 28081, 30011, 31489, 33533, 35617, 37811, 39461, 41759, 44699, 45293, 60899, 68819, 71059, 78007, 83639, 84457, 86111
Offset: 1
Keywords
Examples
311 is in the sequence because 311 is prime, nextprime(311)=313, and 311+313 = 624 = 24*(24+2).
Links
- Harvey P. Dale, Table of n, a(n) for n = 1..500
Programs
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Mathematica
Select[Partition[Prime[Range[9000]],2,1],IntegerQ[Sqrt[1+Total[#]]-1]&] [[All,1]] (* Harvey P. Dale, May 15 2017 *)
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PARI
{k=2;while(k<10^5,l=nextprime(k+1);if(issquare(k+l+1),print1(k,", "));k=l)}