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Or, numbers n such that sum of 5 consecutive primes squared, starting with p(n), ends with 5.

Unlike the average of two, three, four and six successive primes squared (with initial indices > 1,2,1,2, respectively), the average of five successive primes squared is rarely an integer.

Cases of sums ending with 5 are much less numerous than cases with 1, 3, 7 and 9.

E.g. for the first 20000, sums with final digits 1, 3, 5, 7 and 9 are 7238, 2380, 466, 2529 and 7386 (and 1 case with final 8, 208=A131686(1)). And for first 200000 sums the corresponding numbers are 71166, 25820, 5956, 26075, 70982.

The explanation of this "deficiency of final 5's" is simple: assuming that final digits {1,3,7,9} of primes are equally often, we get that probabilities for final digits {1,3,5,7,9} of sum of squares of five primes are {10/32,5/32,2/32,5/32,10/32}.