A097785 Counterexamples to the conjecture that an even, prime-indexed triangular plus 1 equals a prime or that an odd, prime-indexed triangular minus 2 equals a prime.

497, 1771, 2279, 3161, 3487, 5149, 5357, 5993, 6439, 8129, 9451, 9731, 11477, 15049, 16469, 18337, 19901, 25879, 26333, 28681, 29159, 34717, 40187, 43069, 48517, 50401, 54947, 60379, 61073, 62479, 67529, 69749, 72011, 73537, 79001, 88829

Offset: 1

Author

Alonso del Arte and Robert G. Wilson v, Aug 24 2004

Keywords

• nonn

Comments

In the entry for 496, Wells remarks that it is the smallest counterexample to the conjecture that an even, prime-indexed triangular plus 1 equals a prime, since 497 is not prime.

References

• David Wells, The Penguin Dictionary of Curious and Interesting Numbers.

Crossrefs

Cf. A096333.

Programs

Mathematica

tri[n_] := n(n + 1)/2; tp = Table[ tri[ Prime[n]], {n, 2, 85}]; f[n_] := If[ OddQ[n], n - 2, n + 1]; Select[f /@ tp, Not[ PrimeQ[ # ]] &]