A383350 a(n) is the smallest integer k such that there are k+i groups of order a(n)+i, for i=1,...,n.

0, 2, 72, 72, 2814120, 29436120

Offset: 1

Author

Robin Jones, Apr 24 2025

Keywords

• nonn
• fini
• more

Comments

The sequence is finite. For any multiple of 32, there are more than 32 groups of that order. Thus, the sequence 1,2,...,32 can't appear in A000001, and this sequence is at most 31 terms long.

The sequence is either 6 or 7 terms long. This can be shown by first showing every entry of A373650 is congruent to 24 mod 48. It then follows that if n is such that A000001(n+i) = i for i=1,2,3,4, then n+8 is a multiple of 16. But then A000001(n+8) >= 14, so we can't have A000001(n+i) = i for i=1,2,3,4,8.

From a(2) onwards, each entry is a multiple of 24, but not a multiple of 48.

a(7) > 223000000 if it exists.

Each entry is congruent to 0, 2 or 4 modulo 5.

Examples

			a(1) = 0 since there is 1 group of order 1.
a(2) = 2 since there is 1 group of order 3, 2 groups of order 4.
		

Crossrefs

Cf. A373648, A373649, A373650, A381335.