A293622 Fermat pseudoprimes to base 2 that are triangular.

561, 2701, 4371, 8911, 10585, 18721, 33153, 41041, 49141, 93961, 104653, 115921, 157641, 226801, 289941, 314821, 334153, 534061, 665281, 721801, 831405, 873181, 915981, 1004653, 1373653, 1537381, 1755001, 1815465, 1987021, 2035153, 2233441, 2284453, 3059101

Offset

1,1

Comments

Rotkiewicz proved that this sequence is infinite.

Intersection of A001567 and A000217.

Supersequence of A290945 (triangular Carmichael numbers).

All values of A098025(n)*(2*A098025(n)-1) are terms in this sequence.

The corresponding indices of the triangular numbers are 33, 73, 93, 133, 145, 193, 257, 286, 313, 433, 457, 481, 561, 673, 761, 793, 817, ...

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Andrzej Rotkiewicz, Sur les nombres pseudopremiers triangulaires, Elemente der Mathematik, Vol. 19 (1964), pp. 82-83.

Example

2701 = 73 * 74 / 2 = 37 * 73 is in the sequence since it is triangular and composite, and 2^2700 == 1 (mod 2701).

Mathematica

t[n_]:=n(n+1)/2; Select[t[Range[3, 10^4]], PowerMod[2, (# - 1), # ] == 1 &]

Prog

(PARI) forcomposite(c=1, 31*10^5, if(Mod(2, c)^(c-1)==1 && ispolygonal(c, 3), print1(c, ", "))) \\ Felix Fröhlich, Oct 14 2017

Crossrefs

Cf. A000217, A001567, A098025, A290945.

Sequence in context: A110889 A205947 A290692 * A322130 A354609 A207080

Adjacent sequences: A293619 A293620 A293621 * A293623 A293624 A293625

Keyword

nonn

Author

Amiram Eldar, Oct 13 2017

Status

approved