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Old 2021-08-08, 06:03   #3
sweety439
 
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"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

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Code:
k mod 12        such k-values
0      A027856 except 6 and 18 (i.e. A027856 except the numbers not divisible by 4)
1      A325255+1 except 3 and 5
2      26, 242, 1326168790943636873463383702999509006710931275809481594345135568419247032683280476801020577006926016883473704238442000000602205815896338796816029291628752316502980283213233056177518129990821225531587921003213821170980172679786117182128182482511664415807616402 (conjectured no others)
3      27, 243, 2187, 1594323 (conjectured no others)
4      16 (power-of-2-related numbers are proven no others because of algebra factors), 28 (power-of-3-related numbers are conjectured no others)
5      53, 4373 (conjectured no others)
6      6, 18 (conjectured no others)
7      19, 163, 487, 86093443 (conjectured no others)
8      32, 128, 8192, 131072, 524288, 2147483648, 2305843009213693952, 170141183460469231731687303715884105728 (conjectured no others)
9      81 (proven no others because of algebra factors)
10      10, 82 (conjectured no others)
11      A327240-1 except 5 and 7
Thus it is conjectured to exist infinitely many such k-values, however, all but finitely many such k-values are in A027856, A325255+1, or A327240-1 (thus, all but finitely many such k-values have one of k, k-1, k+1 divisible by 12)

Last fiddled with by sweety439 on 2021-08-08 at 06:23
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