A355970 Primes p such that p^2 is the concatenation of x and 2*x+1 for some x.

5, 7, 67, 28573, 666667, 31578949, 64912283, 66666667, 666666667, 66666666667, 29083665338647, 31772053083528493, 50819672131147541, 4299928432854102613, 6811594202898550727, 66666666666666666667, 29136816792745854416111, 46823891622677827205227, 66666666666666666666667

Offset

1,1

Links

Table of n, a(n) for n=1..19.

Example

a(3) = 67 is a term because it is prime and 67^2 = 4489 is the concatenation of 44 and 2*44+1=89.

Maple

dcat:=proc(a, b) a*10^(1+ilog10(b))+b end proc:
f:= proc(t) local s;
if not issqr(t) then return NULL fi;
s:=sqrt(t);
if isprime(s) then return s fi
end proc:
map(f, [seq(dcat(x, 2*x+1), x=1..5*10^7)]);

Crossrefs

Contains A093170.

Cf. A309808, A309828.

Sequence in context: A077780 A307361 A260829 * A130189 A180755 A073624

Adjacent sequences: A355967 A355968 A355969 * A355971 A355972 A355973

Keyword

nonn,base

Author

J. M. Bergot and Robert Israel, Jul 21 2022

Extensions

More terms from Jinyuan Wang, Jul 21 2022

Status

approved