A364359 Primes that are the concatenation of a square and a prime that is the concatenation of two squares.

419, 911, 919, 941, 1181, 1499, 1619, 1811, 4919, 8111, 9181, 9491, 9811, 11699, 12119, 12251, 14411, 14419, 16481, 16811, 19001, 22511, 22541, 32411, 32441, 36251, 44111, 44119, 44729, 49499, 49811, 52919, 57641, 64499, 64811, 67619, 72911, 81181, 90011, 90019, 91009, 92251, 94441, 97841, 98419

Offset

1,1

Comments

Primes that are the concatenation of a square and a member of A167535.

Links

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

Example

a(5) = 1181 is a term because it is the concatenation of 1^2 = 1, 1^2 =1 and 9^2 = 81, and 181 and 1181 are primes.

Maple

for d from 1 to 3 do
  m1:= ceil(10^((d-1)/2));
  m2:= floor(sqrt(10^d - 1));
  S[d]:= {seq(i^2, i=m1..m2)};
  if m1::even then m1:= m1+1 fi;
  So[d]:= {seq(i^2, i=m1..m2, 2)};
od:
for d from 2 to 4 do P2[d]:= select(isprime, {seq(seq(seq(10^i*s+t, t=So[i]), s=S[d-i]), i=1..d-1)}) od:
for d from 3 to 5 do P3[d]:= select(isprime, {seq(seq(seq(10^i*s+t, t=P2[i]), s=S[d-i]), i=2..d-1)}) od:
sort([seq](op(P3[d]), d=3..5));

Crossrefs

Cf. A167535.

Sequence in context: A142281 A242281 A142733 * A060230 A255097 A130737

Adjacent sequences: A364356 A364357 A364358 * A364360 A364361 A364362

Keyword

nonn,base

Author

Robert Israel, Oct 20 2023

Status

approved