%I #14 Apr 02 2019 19:16:10

%S 2,17,347,521,10601,32027,39569,58061,62969,100469,109541,120401,

%T 398129,426383,434261,829883,896771,935063,1190261,1216583,1261109,

%U 1559963,1697771,2105381,2128649,2505857,2778851,2886563,2920649,3051977,3157703,3636617,4068257,5139257,5480249,5650097,5938931

%N Primes p such that p + A007953(p) is the square of a prime.

%C All terms == 2 (mod 3).

%C More than one prime p can have the same value of p + A007953(p), e.g. 528677993 + A007953(52867793) = 528678011 + A007953(528678011) = 22993^2.

%H Robert Israel, <a href="/A307315/b307315.txt">Table of n, a(n) for n = 1..10000</a>

%e a(3)= 347 is in the sequence because 347+3+4+7=361=19^2 and 347 and 19 are primes.

%p f:= proc(q) local m,d,nmin;

%p m:= q^2;

%p d:= ilog10(m)+1;

%p nmin:= m - 9*d;

%p nmin:= nmin + ((5-nmin) mod 6);

%p op(select(t -> t + convert(convert(t,base,10),`+`)=m and isprime(t), {seq(n, n=nmin .. m-2, 6)}))

%p end proc:

%p f(2):= 2:

%p sort(map(f, [seq(ithprime(i),i=1..2000)]));

%o (PARI) is(n) = my(x=n+sumdigits(n)); isprimepower(x)==2

%o forprime(p=1, 6e6, if(is(p), print1(p, ", "))) \\ _Felix Fröhlich_, Apr 02 2019

%Y Subsequence of A242368.

%Y Cf. A007953, A062028, A228195.

%K nonn,base

%O 1,1

%A _Robert Israel_ and _Will Gosnell_, Apr 02 2019