A292284 Numbers n such that 2n+1 is prime, 2n+3 is square, and 2n+5 is triangular.

83, 1103, 98123, 1275203, 1471585499, 130674477863, 1698208392983, 728880893315750472460743125221814632790855997983, 14557044964961408694308418152479413877871536090878805525883

Offset

1,1

Comments

The first 5 terms are primes of the form 6k+5.

a(17) has 1559 digits and a(18) > 10^3000, if it exists. - Giovanni Resta, Sep 15 2017

Links

Table of n, a(n) for n=1..9.

Example

83 is a term as 2*83+1=167 (prime), 2*83+3=169=(13)^2 (square), and 2*83+5=171 (triangular).

Mathematica

Select[Range[10^11], PrimeQ[2#+1] && IntegerQ@Sqrt[2#+3]&& OddQ@Sqrt[8(2#+5)+1]&]

Prog

(PARI) for(n=1, 10^11, isprime(2*n+1) && issquare(2*n+3)&& ispolygonal(2*n+5, 3) && print1(n", "))

Crossrefs

Cf. A000040 (primes), A000290 (squares), A000217 (triangular numbers).

Sequence in context: A128950 A068851 A250083 * A195893 A233332 A175662

Adjacent sequences: A292281 A292282 A292283 * A292285 A292286 A292287

Keyword

nonn

Author

Waldemar Puszkarz, Sep 14 2017

Extensions

a(6)-a(9) from Giovanni Resta, Sep 15 2017

Status

approved