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A376163
Positions of adjacent non-prime-powers (inclusive, so 1 is a prime-power) differing by 1.
1
4, 7, 8, 14, 15, 16, 18, 19, 22, 23, 26, 27, 29, 30, 31, 32, 35, 37, 39, 40, 43, 44, 45, 46, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 62, 63, 66, 67, 70, 71, 73, 74, 75, 76, 77, 78, 80, 81, 84, 86, 87, 88, 89, 92, 93, 94, 95, 96, 97, 98, 99, 102, 103, 104, 105
OFFSET
1,1
EXAMPLE
The non-prime-powers (inclusive) are 6, 10, 12, 14, 15, 18, 20, 21, 22, 24, ... which increase by 1 after positions 4, 7, 8, ...
MATHEMATICA
ce=Select[Range[2, 100], !PrimePowerQ[#]&];
Select[Range[Length[ce]-1], ce[[#+1]]==ce[[#]]+1&]
CROSSREFS
For prime-powers inclusive (A000961) we have A375734, differences A373671.
For nonprime numbers (A002808) we have A375926, differences A373403.
For prime-powers exclusive (A246655) we have A375734(n+1) + 1.
First differences are A373672.
The exclusive version is a(n) - 1 = A375713.
Positions of 1's in A375735.
For non-perfect-powers we have A375740.
Prime-powers inclusive:
- terms: A000961
- differences: A057820
Non-prime-powers inclusive:
- terms: A361102
- differences: A375708
A000040 lists all of the primes, differences A001223.
A007916 lists non-perfect-powers, differences A375706.
Sequence in context: A291402 A328792 A073435 * A324854 A086987 A051219
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 13 2024
STATUS
approved