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A282690 a(n) is the smallest number m, such that m+n is the next prime and m-n is the previous prime.

%I A282690 #14 Jul 29 2020 05:52:00
%S A282690 4,5,26,93,144,53,120,1839,532,897,1140,211,2490,2985,4312,5607,1344,
%T A282690 9569,30612,19353,16162,15705,81486,16787,31932,19635,35644,82101,
%U A282690 44322,43361,34092,89721,162176,134547,173394,31433,404634,212739,188068,542643,265662
%N A282690 a(n) is the smallest number m, such that m+n is the next prime and m-n is the previous prime.
%H A282690 Daniel Suteu, <a href="/A282690/b282690.txt">Table of n, a(n) for n = 1..100</a>
%e A282690 For n = 6, a(6) = 53, because the next prime after 53 is 59 and the previous prime before 53 is 47, where both have an equal distance of 6 from 53, which is the smallest number with this property.
%t A282690 Table[k = 1; While[Nand[k - n == NextPrime[k, -1], k + n == NextPrime@ k], k++]; k, {n, 41}] (* _Michael De Vlieger_, Feb 20 2017 *)
%o A282690 (Perl)
%o A282690 use ntheory qw(:all);
%o A282690 for (my $k = 1 ; ; ++$k) {
%o A282690     for (my $n = 1 ; ; ++$n) {
%o A282690         my $p = prev_prime($n) || next;
%o A282690         my $q = next_prime($n);
%o A282690         if ($n-$p == $k and $q-$n == $k) {
%o A282690             printf("%s %s\n", $k, $n);
%o A282690             last;
%o A282690         }
%o A282690     }
%o A282690 }
%Y A282690 Cf. A087378, A087711, A282687.
%K A282690 nonn
%O A282690 1,1
%A A282690 _Daniel Suteu_, Feb 20 2017