A374380 Numbers b such that the base-b expansion of Pi has two equal digits immediately after the radix point.

2, 8, 114, 227, 340, 453, 566, 679, 33103, 66318, 265382, 1360121, 1725034, 25510583, 78256780, 209259756, 340262732, 1151791170, 1963319608, 6701487260, 13402974519, 20104461778, 26805949037, 33507436296, 40208923555, 46910410814, 53611898073, 574364584668

Offset: 1

Author

Mike Keith, Jul 06 2024

Keywords

• nonn

Comments

The probability that this occurs in a random base-b number is 1/b, so the divergence of the harmonic series suggests this sequence is infinite. a(28) = 574364584668 is the largest term < 10^12.

If 1 is added to terms of A002486, many of the resulting numbers (roughly 60%) are terms of this sequence. - Mike Keith, Jul 28 2024

Examples

			2 is a term since Pi in base 2 is 11.00... which has two equal digits 0,0.
114 is a term since Pi in base 114 is 3.(16)(16)... which has two equal "digits" 16 and 16.
		

Crossrefs

Cf. A000796 (Pi), A336017 (second digit after radix point), A002486 (continued fraction convergent denominators).