A307315 Primes p such that p + A007953(p) is the square of a prime.

2, 17, 347, 521, 10601, 32027, 39569, 58061, 62969, 100469, 109541, 120401, 398129, 426383, 434261, 829883, 896771, 935063, 1190261, 1216583, 1261109, 1559963, 1697771, 2105381, 2128649, 2505857, 2778851, 2886563, 2920649, 3051977, 3157703, 3636617, 4068257, 5139257, 5480249, 5650097, 5938931

Offset: 1

Author

Robert Israel and Will Gosnell, Apr 02 2019

Keywords

• nonn
• base

Comments

All terms == 2 (mod 3).

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

Examples

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

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A242368.

Cf. A007953, A062028, A228195.

Programs

Maple

f:= proc(q) local m,d,nmin;
  m:= q^2;
  d:= ilog10(m)+1;
  nmin:= m - 9*d;
  nmin:= nmin + ((5-nmin) mod 6);
  op(select(t ->  t + convert(convert(t,base,10),`+`)=m and isprime(t), {seq(n, n=nmin .. m-2, 6)}))
end proc:
f(2):= 2:
sort(map(f, [seq(ithprime(i),i=1..2000)]));

PARI

is(n) = my(x=n+sumdigits(n)); isprimepower(x)==2
forprime(p=1, 6e6, if(is(p), print1(p, ", "))) \\ Felix Fröhlich, Apr 02 2019