A278139 Primes, starting with a(1)=2, whose successive differences are increasing triangular numbers.
2, 3, 13, 41, 107, 227, 503, 881, 1409, 2039, 2819, 3947, 5273, 6869, 8699, 11549, 15377, 19937, 24593, 30809, 38069, 47939, 58379, 69257, 82787, 98897, 115733, 133499, 152027, 172127, 192833, 218711, 247391, 279269, 315047, 355517, 399473, 444623
Offset: 1
Programs
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Mathematica
lst={1};p[1]=2;p[n_]:=p[n]=Module[{i=Last[lst]+1}, While[!PrimeQ[p[n-1]+i*(i-1)/2],i++];AppendTo[lst,i];p[n-1]+i*(i-1)/2]; p/@Range[50]