A333254 -id:A333254 - cp's OEIS frontend

A376653 Sorted positions of first appearances in the second differences of consecutive prime-powers inclusive (A000961).

1, 4, 5, 10, 12, 18, 25, 45, 47, 48, 60, 68, 69, 71, 80, 118, 121, 178, 179, 199, 206, 207, 216, 244, 245, 304, 325, 327, 402, 466, 484, 605, 801, 880, 939, 1033, 1055, 1077, 1234, 1281, 1721, 1890, 1891, 1906, 1940, 1960, 1962, 2257, 2290, 2410, 2880, 3150

Offset: 1

Gus Wiseman, Oct 06 2024

nonn

			The prime-powers inclusive (A000961) are:
  1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, 27, 29, 31, 32, 37, 41, 43, ...
with first differences (A057820):
  1, 1, 1, 1, 2, 1, 1, 2, 2, 3, 1, 2, 4, 2, 2, 2, 2, 1, 5, 4, 2, 4, 2, 4, 6, 2, 3, ...
with first differences (A376596):
  0, 0, 0, 1, -1, 0, 1, 0, 1, -2, 1, 2, -2, 0, 0, 0, -1, 4, -1, -2, 2, -2, 2, 2, ...
with first appearances (A376653):
  1, 4, 5, 10, 12, 18, 25, 45, 47, 48, 60, 68, 69, 71, 80, 118, 121, 178, 179, 199, ...

For first differences we had A057820, sorted firsts A376340(n)+1 (except first term).
These are the sorted positions of first appearances in A376596.
The exclusive version is a(n) - 1 = A376654(n), except first term.
For squarefree instead of prime-power we have A376655.
A000961 lists prime-powers inclusive, exclusive A246655.
A001597 lists perfect-powers, complement A007916.
A023893 and A023894 count integer partitions into prime-powers, factorizations A000688.
A064113 lists positions of adjacent equal prime gaps.
For prime-powers inclusive: A057820 (first differences), A376597 (inflections and undulations), A376598 (nonzero curvature).
For second differences: A036263 (prime), A073445 (composite), A376559 (perfect-power), A376562 (non-perfect-power), A376590 (squarefree), A376593 (nonsquarefree), A376599 (non-prime-power).
Cf. A053707, A069623, A093555, A174965, A251092, A333254, A361102.

q=Differences[Select[Range[100],#==1||PrimePowerQ[#]&],2];
Select[Range[Length[q]],!MemberQ[Take[q,#-1],q[[#]]]&]

A333252 Lengths of maximal strictly decreasing subsequences in the sequence of prime gaps (A001223).

Original entry on oeis.org

1, 1, 1, 2, 2, 1, 2, 3, 1, 1, 2, 3, 2, 1, 3, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 3, 1, 2, 2, 1, 2, 3, 1, 3, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 2, 2, 2, 1, 3, 1, 3, 2, 1, 2, 2, 2, 2, 1, 2, 2, 1, 3, 3, 1, 1, 2, 2, 1, 1, 2, 3, 2, 3, 2, 2, 2, 2, 2, 1, 3, 1, 3, 1, 2, 1

Offset: 1

Gus Wiseman, Mar 18 2020

nonn

Prime gaps are differences between adjacent prime numbers.

			The prime gaps split into the following strictly decreasing subsequences: (1), (2), (2), (4,2), (4,2), (4), (6,2), (6,4,2), (4), (6), (6,2), (6,4,2), (6,4), (6), (8,4,2), (4,2), (4), (14,4), (6,2), (10,2), (6), (6,4), (6), ...

Wikipedia, Longest increasing subsequence

The weakly decreasing version is A333212.
The weakly increasing version is A333215.
The unequal version is A333216.
First differences of A333230 (if the first term is 0).
The strictly increasing version is A333253.
The equal version is A333254.
Prime gaps are A001223.
Strictly decreasing runs of compositions in standard order are A124769.
Positions of strict descents in the sequence of prime gaps are A258026.
Cf. A000040, A064113, A084758, A124764, A124766, A258025, A333213, A333214, A333252, A333256.

Length/@Split[Differences[Array[Prime,100]],#1>#2&]//Most

Partial sums are A333230. The partial sum up to but not including the n-th one is A333381(n - 1).

A376560 Points of upward concavity in the sequence of perfect-powers (A001597). Positives of A376559.

Original entry on oeis.org

1, 3, 4, 6, 8, 9, 10, 11, 12, 15, 16, 17, 20, 22, 23, 26, 27, 28, 31, 32, 33, 34, 35, 36, 37, 38, 41, 42, 43, 44, 46, 47, 48, 49, 50, 53, 54, 55, 57, 58, 60, 61, 62, 63, 64, 65, 67, 68, 69, 72, 73, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 88, 89, 90, 91

Offset: 1

Gus Wiseman, Sep 30 2024

nonn

These are points at which the second differences are positive.
Perfect-powers (A001597) are numbers with a proper integer root.
Note that, for some sources, upward concavity is negative curvature.

			The perfect powers (A001597) are:
  1, 4, 8, 9, 16, 25, 27, 32, 36, 49, 64, 81, 100, 121, 125, 128, 144, 169, 196, ...
with first differences (A053289):
  3, 4, 1, 7, 9, 2, 5, 4, 13, 15, 17, 19, 21, 4, 3, 16, 25, 27, 20, 9, 18, 13, 33, ...
with first differences (A376559):
  1, -3, 6, 2, -7, 3, -1, 9, 2, 2, 2, 2, -17, -1, 13, 9, 2, -7, -11, 9, -5, 20, 2, ...
with positive positions (A376560):
  1, 3, 4, 6, 8, 9, 10, 11, 12, 15, 16, 17, 20, 22, 23, 26, 27, 28, 31, 32, 33, 34, ...

Robert Israel, Table of n, a(n) for n = 1..10000
Gus Wiseman, Points of upward concavity in the perfect-powers.

The version for A000002 is A022297, complement A025505. See also A054354, A376604.
For first differences we have A053289, union A023055, firsts A376268, A376519.
For primes instead of perfect-powers we have A258025.
These are positions of positive terms in A376559.
For downward concavity we have A376561 (probably the complement).
A001597 lists the perfect-powers.
A064113 lists positions of adjacent equal prime gaps.
A333254 gives run-lengths of differences between consecutive primes.
Second differences: A036263 (prime), A073445 (composite), A376559 (perfect-power), A376562 (non-perfect-power), A376590 (squarefree), A376593 (nonsquarefree), A376596 (prime-power), A376599 (non-prime-power).
Cf. A006549, A025475, A030173, A045542, A052410, A053707, A054819, A069623, A174965, A216765, A251092, A376308.

N:= 10^6: # to use perfect powers <= N
S:= {1,seq(seq(i^j,j=2..floor(log[i](N))),i=2..isqrt(N))}:
L:= sort(convert(S,list)):
DL:= L[2..-1]-L[1..-2]:
D2L:= DL[2..-1]-DL[1..-2]:
select(i -> D2L[i]>0, [$1..nops(D2L)]); # Robert Israel, Dec 01 2024

perpowQ[n_]:=n==1||GCD@@FactorInteger[n][[All,2]]>1;
Join@@Position[Sign[Differences[Select[Range[1000],perpowQ],2]],1]

A376654 Sorted positions of first appearances in the second differences of consecutive prime-powers exclusive (A246655).

Original entry on oeis.org

3, 4, 9, 11, 17, 24, 44, 46, 47, 59, 67, 68, 70, 79, 117, 120, 177, 178, 198, 205, 206, 215, 243, 244, 303, 324, 326, 401, 465, 483, 604, 800, 879, 938, 1032, 1054, 1076, 1233, 1280, 1720, 1889, 1890, 1905, 1939, 1959, 1961, 2256, 2289, 2409, 2879, 3149

Offset: 1

Gus Wiseman, Oct 06 2024

nonn

			The prime-powers exclusive (A246655) are:
  2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, 27, 29, 31, 32, 37, 41, 43, 47, ...
with first differences (A057820 except first term) :
  1, 1, 1, 2, 1, 1, 2, 2, 3, 1, 2, 4, 2, 2, 2, 2, 1, 5, 4, 2, 4, 2, 4, 6, 2, 3, 3, ...
with first differences (A376596 except first term):
  0, 0, 1, -1, 0, 1, 0, 1, -2, 1, 2, -2, 0, 0, 0, -1, 4, -1, -2, 2, -2, 2, 2, -4, ...
with first appearances (A376654):
  1, 3, 4, 9, 11, 17, 24, 44, 46, 47, 59, 67, 68, 70, 79, 117, 120, 177, 178, 198, ...

For first differences we have A376340.
These are the sorted positions of first appearances in A376596 except first term.
The inclusive version is a(n) + 1 = A376653(n), except first term.
For squarefree instead of prime-power we have A376655.
A000961 lists prime-powers inclusive, exclusive A246655.
A001597 lists perfect-powers, complement A007916.
A023893 and A023894 count integer partitions into prime-powers, factorizations A000688.
For prime-powers inclusive: A057820 (first differences), A376597 (inflections and undulations), A376598 (nonzero curvature).
For second differences: A036263 (prime), A073445 (composite), A376559 (perfect-power), A376562 (non-perfect-power), A376590 (squarefree), A376593 (nonsquarefree), A376599 (non-prime-power).
Cf. A025475, A053707, A057820, A064113, A069623, A093555, A174965, A333254, A336416, A361102.

q=Differences[Select[Range[1000],PrimePowerQ[#]&],2];
Select[Range[Length[q]],!MemberQ[Take[q,#-1],q[[#]]]&]

A333490 First index of unequal prime quartets.

Original entry on oeis.org

7, 8, 10, 11, 13, 17, 18, 19, 20, 22, 23, 24, 28, 30, 31, 32, 34, 40, 42, 44, 47, 49, 50, 51, 52, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 75, 76, 78, 79, 82, 83, 85, 86, 87, 89, 90, 91, 94, 95, 96, 97, 98, 99, 104, 111, 112, 113, 114, 115, 116, 119

Offset: 1

Gus Wiseman, May 15 2020

nonn

Let g(i) = prime(i + 1) - prime(i). These are numbers k such that g(k), g(k + 1), and g(k + 2) are all different.

			The first 10 unequal prime quartets:
  17  19  23  29
  19  23  29  31
  29  31  37  41
  31  37  41  43
  41  43  47  53
  59  61  67  71
  61  67  71  73
  67  71  73  79
  71  73  79  83
  79  83  89  97
For example, 83 is the 23rd prime, and the primes (83,89,97,101) have differences (6,8,4), which are all distinct, so 23 is in the sequence.

Primes are A000040.
Prime gaps are A001223.
Second prime gaps are A036263.
Indices of unequal rows of A066099 are A233564.
Lengths of maximal anti-run subsequences of prime gaps are A333216.
Lengths of maximal runs of prime gaps are A333254.
Maximal anti-runs in standard compositions are counted by A333381.
Indices of anti-run rows of A066099 are A333489.
Strictly decreasing prime quartets are A054804.
Strictly increasing prime quartets are A054819.
Equal prime quartets are A090832.
Weakly increasing prime quartets are A333383.
Weakly decreasing prime quartets are A333488.
Unequal prime quartets are A333490 (this sequence).
Partially unequal prime quartets are A333491.
Positions of adjacent equal prime gaps are A064113.
Positions of strict ascents in prime gaps are A258025.
Positions of strict descents in prime gaps are A258026.
Positions of adjacent unequal prime gaps are A333214.
Positions of weak ascents in prime gaps are A333230.
Positions of weak descents in prime gaps are A333231.
Cf. A006560, A031217, A054800, A059044, A084758, A089180, A124767, A333215.

ReplaceList[Array[Prime,100],{_,x_,y_,z_,t_,_}/;y-x!=z-y!=t-z:>PrimePi[x]]

A333491 First index of partially unequal prime quartets.

Original entry on oeis.org

3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 37, 40, 41, 42, 43, 44, 47, 48, 49, 50, 51, 52, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 74, 75, 76, 77, 78, 79, 80, 81, 82

Offset: 1

Gus Wiseman, May 15 2020

nonn

Let g(i) = prime(i + 1) - prime(i). These are numbers k such that g(k) != g(k + 1) != g(k + 2), but we may have g(k) = g(k + 2).

			The first 10 partially unequal prime quartets:
   5  7 11 13
   7 11 13 17
  11 13 17 19
  13 17 19 23
  17 19 23 29
  19 23 29 31
  23 29 31 37
  29 31 37 41
  31 37 41 43
  37 41 43 47

Primes are A000040.
Prime gaps are A001223.
Second prime gaps are A036263.
Indices of unequal rows of A066099 are A233564.
Lengths of maximal anti-runs of prime gaps are A333216.
Lengths of maximal runs of prime gaps are A333254.
Maximal anti-runs in standard compositions are counted by A333381.
Indices of anti-run rows of A066099 are A333489.
Strictly decreasing prime quartets are A054804.
Strictly increasing prime quartets are A054819.
Equal prime quartets are A090832.
Weakly increasing prime quartets are A333383.
Weakly decreasing prime quartets are A333488.
Unequal prime quartets are A333490.
Partially unequal prime quartets are A333491 (this sequence).
Positions of adjacent equal prime gaps are A064113.
Positions of strict ascents in prime gaps are A258025.
Positions of strict descents in prime gaps are A258026.
Positions of adjacent unequal prime gaps are A333214.
Positions of weak ascents in prime gaps are A333230.
Positions of weak descents in prime gaps are A333231.
Cf. A006560, A031217, A054800, A059044, A084758, A089180, A124767, A333215.

ReplaceList[Array[Prime,100],{_,x_,y_,z_,t_,_}/;y-x!=z-y&&z-y!=t-z:>PrimePi[x]]
PrimePi[#]&/@(Select[Partition[Prime[Range[90]],4,1],#[[2]]-#[[1]]!=#[[3]]-#[[2]]&&#[[3]]-#[[2]]!=#[[4]]-#[[3]]&][[;;,1]]) (* Harvey P. Dale, Aug 05 2025 *)

A376309 Run-lengths of the sequence of first differences of prime-powers.

Original entry on oeis.org

3, 1, 2, 2, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 1, 2

Offset: 1

Gus Wiseman, Sep 22 2024

nonn

			The sequence of prime-powers (A246655) is:
  2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, 27, 29, 31, 32, 37, ...
The sequence of first differences (A057820) of prime-powers is:
  1, 1, 1, 2, 1, 1, 2, 2, 3, 1, 2, 4, 2, 2, 2, 2, 1, 5, 4, 2, 4, 2, 4, ...
with runs:
  (1,1,1),(2),(1,1),(2,2),(3),(1),(2),(4),(2,2,2,2),(1),(5),(4),(2),(4), ...
with lengths A376309 (this sequence).

Antti Karttunen, Table of n, a(n) for n = 1..20000

For runs of prime-powers increasing by one we have A174965.
For primes instead of prime-powers we have A333254.
For squarefree numbers instead of prime-powers we have A376306.
For compression instead of run-lengths we have A376308.
For run-sums instead of run-lengths we have A376310.
For positions of first appearances we have A376341, sorted A376340.
A000040 lists the prime numbers, differences A001223.
A000961 and A246655 list prime-powers, first differences A057820.
A003242 counts compressed compositions, ranks A333489.
A005117 lists squarefree numbers, differences A076259.
A024619 and A361102 list non-prime-powers, first differences A375708.
A116861 counts partitions by compressed sum, by compressed length A116608.
A124767 counts runs in standard compositions, anti-runs A333381.
A238130, A238279, A333755 count compositions by number of runs.
A274174 counts contiguous compositions, ranks A374249.
A373948 encodes compression using compositions in standard order.
Cf. A001597, A006549, A025475, A037201, A053289, A110969, A120430, A251092, A373822, A375706.

Length/@Split[Differences[Select[Range[100],PrimePowerQ]]]

up_to = 20000;
A376309list(up_to) = { my(v=vector(up_to), ppp=2, pd=1, d, rl=0, k=2, i=0); while(i<#v, k++; if(isprimepower(k), d = k-ppp; ppp = k; if(d == pd, rl++, i++; v[i] = rl; rl = 1; pd = d))); (v); };
v376309 = A376309list(up_to);
A376309(n) = v376309[n]; \\ Antti Karttunen, Jan 18 2025

More terms from Antti Karttunen, Jan 18 2025

A373825 Position of first appearance of n in the run-lengths (differing by 0) of the run-lengths (differing by 2) of the odd primes.

Original entry on oeis.org

1, 2, 13, 11, 105, 57, 33, 69, 59, 29, 227, 129, 211, 341, 75, 321, 51, 45, 407, 313, 459, 301, 767, 1829, 413, 537, 447, 1113, 1301, 1411, 1405, 2865, 1709, 1429, 3471, 709, 2543, 5231, 1923, 679, 3301, 2791, 6555, 5181, 6345, 11475, 2491, 10633

Offset: 1

Gus Wiseman, Jun 21 2024

nonn

Positions of first appearances in A373819.

			The runs of odd primes differing by 2 begin:
   3   5   7
  11  13
  17  19
  23
  29  31
  37
  41  43
  47
  53
  59  61
  67
  71  73
  79
with lengths:
3, 2, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2, ...
which have runs beginning:
  3
  2 2
  1
  2
  1
  2
  1 1
  2
  1
  2
  1 1 1 1
  2 2
  1 1 1
with lengths:
1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 4, 2, 3, 2, 4, 3, ...
with positions of first appearances a(n).

Firsts of A373819 (run-lengths of A251092).
For antiruns we have A373827 (sorted A373826), firsts of A373820, run-lengths of A027833 (partial sums A029707, firsts A373401, sorted A373402).
The sorted version is A373824.
A000040 lists the primes.
A001223 gives differences of consecutive primes (firsts A073051), run-lengths A333254 (firsts A335406), run-lengths of run-lengths A373821.
A046933 counts composite numbers between primes.
A065855 counts composite numbers up to n.
A071148 gives partial sums of odd primes.
For prime runs: A001359, A006512, A025584, A067774, A373405, A373406.
For composite runs: A005381, A054265, A068780, A176246, A373403, A373404.
Cf. A006560, A006562, A037201, A038664, A069010, A122535.

t=Length/@Split[Length/@Split[Select[Range[3,10000], PrimeQ],#1+2==#2&]//Most]//Most;
spna[y_]:=Max@@Select[Range[Length[y]],SubsetQ[t,Range[#1]]&];
Table[Position[t,k][[1,1]],{k,spna[t]}]

A376600 Inflection or undulation points in the sequence of non-prime-powers inclusive (A024619).

Original entry on oeis.org

2, 7, 9, 10, 11, 14, 15, 18, 20, 22, 24, 26, 29, 30, 31, 33, 39, 41, 43, 44, 45, 47, 48, 50, 51, 52, 55, 56, 57, 58, 59, 62, 64, 66, 68, 70, 73, 74, 75, 76, 77, 80, 86, 87, 88, 90, 92, 93, 94, 95, 96, 97, 98, 100, 102, 103, 104, 107, 108, 109, 112, 114, 116

Offset: 1

Gus Wiseman, Oct 05 2024

nonn

These are points at which the second differences (A376599) are zero.

Inclusive means 1 is a prime-power but not a non-prime-power. For the exclusive version, add 1 to all terms.

			The non-prime-powers inclusive are (A024619):
  6, 10, 12, 14, 15, 18, 20, 21, 22, 24, 26, 28, 30, 33, 34, 35, 36, 38, 39, 40, ...
with first differences (A375735):
  4, 2, 2, 1, 3, 2, 1, 1, 2, 2, 2, 2, 3, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, ...
with first differences (A376599):
  -2, 0, -1, 2, -1, -1, 0, 1, 0, 0, 0, 1, -2, 0, 0, 1, -1, 0, 1, 0, -1, 0, 1, 0, ...
with zeros at (A376600):
  2, 7, 9, 10, 11, 14, 15, 18, 20, 22, 24, 26, 29, 30, 31, 33, 39, 41, 43, 44, ...

Gus Wiseman, Inflection and undulation points in the non-prime-powers inclusive.

For first differences we had A375735, ones A375713(n)-1.
These are the zeros of A376599.
The complement is A376601.
A000961 lists prime-powers inclusive, exclusive A246655.
A001597 lists perfect-powers, complement A007916.
A024619/A361102 list non-prime-powers inclusive.
A321346/A321378 count integer partitions into non-prime-powers, factorizations A322452.
For non-prime-powers: A375735/A375708 (first differences), A376599 (second differences), A376601 (nonzero curvature).
For second differences: A036263 (prime), A073445 (composite), A376559 (perfect-power), A376562 (non-perfect-power), A376590 (squarefree), A376593 (nonsquarefree), A376596 (prime-power).
Cf. A025475, A053707, A057820, A064113, A093555, A174965, A251092, A333254, A376653, A376654.

Join@@Position[Differences[Select[Range[100], !(#==1||PrimePowerQ[#])&],2],0]

A049579 Numbers k such that prime(k)+2 divides (prime(k)-1)!.

Original entry on oeis.org

4, 6, 8, 9, 11, 12, 14, 15, 16, 18, 19, 21, 22, 23, 24, 25, 27, 29, 30, 31, 32, 34, 36, 37, 38, 39, 40, 42, 44, 46, 47, 48, 50, 51, 53, 54, 55, 56, 58, 59, 61, 62, 63, 65, 66, 67, 68, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95

Offset: 1

Labos Elemer

nonn

Numbers k such that prime(k+1) - prime(k) does not divide prime(k+1) + prime(k). These are the numbers k for which prime(k+1) - prime(k) > 2. - Thomas Ordowski, Mar 31 2022

If we prepend 1, the first differences are A251092 (see also A175632). The complement is A029707. - Gus Wiseman, Dec 03 2024

			prime(4) = 7, 6!+1 = 721 gives residue 1 when divided by prime(4)+2 = 9.

Amiram Eldar, Table of n, a(n) for n = 1..10000

The first differences are A251092 except first term, run-lengths A373819.
The complement is A029707.
Runs of terms differing by one have lengths A027833, min A107770, max A155752.
A000040 lists the primes, differences A001223 (run-lengths A333254, A373821).
A038664 finds the first prime gap of difference 2n.
A046933 counts composite numbers between primes.
A071148 gives partial sums of odd primes.
For prime runs: A001359, A005381, A006512, A025584, A067774, A373403.
Cf. A006560, A006562, A037201, A122535, A175632, A176246, A373820.

pnmQ[n_]:=Module[{p=Prime[n]},Mod[(p-1)!+1,p+2]==1]; Select[Range[ 100],pnmQ] (* Harvey P. Dale, Jun 24 2017 *)

isok(n) = (((prime(n)-1)! + 1) % (prime(n)+2)) == 1; \\ Michel Marcus, Dec 31 2013

Definition edited by Thomas Ordowski, Mar 31 2022

cp's OEIS Frontend

A376653 Sorted positions of first appearances in the second differences of consecutive prime-powers inclusive (A000961).

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A333252 Lengths of maximal strictly decreasing subsequences in the sequence of prime gaps (A001223).

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Formula

A376560 Points of upward concavity in the sequence of perfect-powers (A001597). Positives of A376559.

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Maple

Mathematica

A376654 Sorted positions of first appearances in the second differences of consecutive prime-powers exclusive (A246655).

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Mathematica

A333490 First index of unequal prime quartets.

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Mathematica

A333491 First index of partially unequal prime quartets.

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Mathematica

A376309 Run-lengths of the sequence of first differences of prime-powers.

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Mathematica

PARI

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A373825 Position of first appearance of n in the run-lengths (differing by 0) of the run-lengths (differing by 2) of the odd primes.

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Mathematica

A376600 Inflection or undulation points in the sequence of non-prime-powers inclusive (A024619).

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