A381335 Integers k such that there are i groups of order k+i up to isomorphism, for i=1,2,3,4,5.

2814120, 22411272, 29436120, 46906920, 58734120, 59558520, 71510520, 106822200, 109673064, 117873720, 200250120, 213805272

Offset: 1

Author

Robin Jones, Apr 19 2025

Keywords

• nonn
• hard
• more

Comments

a(13) > 220000000 if it exists.

Each term is a multiple of 24. No terms are multiples of 48.

Each term is congruent to 0, 2 or 4 modulo 5. Terms can't be congruent to 5 modulo 7. I think they also can't be congruent to 3 modulo 7, but I haven't proven that yet.

Examples

			2814120 is in this sequence as there is 1 group of order 2814121 up to isomorphism, 2 of order 2814122, 3 of order 2814123, 4 of order 2814124, 5 of order 2814125.
		

Crossrefs

Cf. A373648 (i=1,2), A373649 (i=1,2,3), A373650 (i=1,2,3,4).