A294652 Positive integers k such that the sum of decimal digits of (4^k - 1) equals 3*k.

1, 2, 3, 4, 6, 7, 8, 10, 12, 13, 14, 20, 23, 24, 25, 26, 27, 28, 34, 36, 41, 46, 65, 71, 74, 83, 86, 89, 92, 111, 120, 235, 238, 253, 297, 366, 446

Offset

1,2

Comments

Integers k such that A007953(4^k - 1) = A008585(k).

No other terms below 10^6.

Conjecture: For k > 446, digsum(4^k - 1) < 3*k. This would mean that no further terms exist in the sequence.

If a(n) is even, then a(n)/2 is in A165722.

Links

Table of n, a(n) for n=1..37.

Example

4^2 - 1 is 15 with sum of digits 6, so 2 is a term.
4^3 - 1 is 63 with sum of digits 9, so 3 is a term.
4^5 - 1 is 1023 with sum of digits 6, so 5 is not a term.

Mathematica

Select[Range[2500], 3# == Total[IntegerDigits[4^# - 1]] &] (* G. C. Greubel, Nov 28 2017 *)

Prog

(PARI) is(n) = 3*n == sumdigits(4^n-1)

Crossrefs

Cf. A007953, A008585, A165722.

Sequence in context: A368747 A336824 A114149 * A352882 A320143 A062974

Adjacent sequences: A294649 A294650 A294651 * A294653 A294654 A294655

Keyword

nonn,base,more

Author

Iain Fox, Nov 27 2017

Status

approved