A242368 -id:A242368 - cp's OEIS frontend

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

Robert Israel and Will Gosnell, Apr 02 2019

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.

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

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

Subsequence of A242368.

Cf. A007953, A062028, A228195.

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)]));

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

A342773 Numbers k such that k + sum of digits of k is a proper prime power.

Original entry on oeis.org

2, 4, 8, 17, 18, 25, 38, 72, 118, 121, 161, 234, 245, 275, 329, 347, 521, 614, 720, 830, 944, 998, 1016, 1318, 1355, 1664, 1829, 2041, 2169, 2183, 2189, 2384, 2786, 3115, 3464, 3710, 4082, 4472, 4891, 4900, 5027, 5315, 6230, 6543, 6836, 7889, 8173, 10190, 10592, 10601, 11435, 11858, 12154, 12752

Offset: 1

J. M. Bergot and Robert Israel, Mar 21 2021

Numbers k such that A062028(k) is in A246547.

Proper prime powers in the sequence include 4, 8, 25, 121. Are there any others?

			a(4) = 17 is a term because 17+1+7 = 25 = 5^2.

Robert Israel, Table of n, a(n) for n = 1..1001

Cf. A062028, A246547. Contains A242368.

filter:= proc(n) local s,F;
   s:= n + convert(convert(n,base,10),`+`);
   F:= ifactors(s)[2];
   nops(F)=1 and F[1][2]>1
end proc:
select(filter, [$1..20000]);

isok(k) = isprimepower(k + sumdigits(k)) > 1; \\ Michel Marcus, Mar 22 2021

cp's OEIS Frontend

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

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