A387523 -id:A387523 - cp's OEIS frontend

A387640 A387523(n) is the a(n)-th prime number.

1, 2, 3, 4, 6, 5, 7, 8, 9, 10, 11, 14, 13, 12, 15, 19, 18, 17, 16, 21, 20, 23, 22, 30, 29, 28, 27, 26, 25, 24, 31, 37, 36, 35, 34, 33, 32, 44, 43, 42, 41, 40, 39, 38, 46, 45, 47, 54, 53, 52, 51, 50, 49, 48, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 68, 67

Offset: 1

Rémy Sigrist, Sep 04 2025

If the conjecture in A387523 is true, then the present sequence is self-inverse.

			a(42) = A000720(A387523(42)) = A000720(173) = 40.

Rémy Sigrist, Table of n, a(n) for n = 1..10949
Rémy Sigrist, PARI program

Cf. A000720, A386482, A387523, A387544.

PARI
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a(n) = A000720(A387523(n)).

A387524 Primes p with property that in A386482 they are immediately preceded by 2p and immediately followed by 3p.

Original entry on oeis.org

3, 7, 11, 19, 31, 47, 131, 317, 947, 4327, 48091, 77237, 158489, 237733, 1973087, 3398221, 4409519

Offset: 1

N. J. A. Sloane, Sep 03 2025

This is in marked contrast to the EKG sequence A064413, where all primes > 2 have this property.

Cf. A064413, A386482, A386483, A387072, A387076, A387077, A387522, A387523.

More terms from Michael De Vlieger, Sep 03 2025

A387634 Indices k such that s(k) is a prime p, s(k-1) = 2p, and s(k+1) = 3p, where s = A386482.

Original entry on oeis.org

5, 11, 24, 31, 57, 76, 236, 479, 1532, 7652, 82123, 129791, 274542, 419569, 3367328, 7002435, 7690249, 45355072

Offset: 1

Michael De Vlieger, Sep 04 2025

			Table of n, a(n), with a(n) = k, listing s(k) and its immediate neighbors:
 n  a(n) = k     s(k-1)      s(k)     s(k+1)
--------------------------------------------
 1         5         6         3          9
 2        11        14         7         21
 3        24        22        11         33
 4        31        38        19         57
 5        57        62        31         93
 6        76        94        47        141
 7       236       262       131        393
 8       479       634       317        951
 9      1532      1894       947       2841
10      7652      8654      4327      12981
11     82123     96182     48091     144273
12    129791    154474     77237     231711
13    274542    316978    158489     475467
14    419569    475466    237733     713199
15   3367328   3946174   1973087    5919261
16   7002435   6796442   3398221   10194663
17   7690249   8819038   4409519   13228557

Cf. A064413, A386482, A386483, A387072, A387076, A387077, A387522, A387523, A387524.

s = Import["https://oeis.org/A386482/b386482.txt", "Data"][[All, -1]]; m = Length[s]; t = TakeWhile[Import["https://oeis.org/A387077/b387077.txt", "Data"][[All, -1]], # <= m &]; Select[t, #1 == 2 #2 && #3 == 3 #2 & @@ s[[# - 1 ;; # + 1]] &] ]

a(18) from Chai Wah Wu, Sep 06 2025

cp's OEIS Frontend

A387640 A387523(n) is the a(n)-th prime number.

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A387524 Primes p with property that in A386482 they are immediately preceded by 2p and immediately followed by 3p.

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Author

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Comments

Crossrefs

Extensions

A387634 Indices k such that s(k) is a prime p, s(k-1) = 2p, and s(k+1) = 3p, where s = A386482.

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Author

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Mathematica

Extensions

cp's OEIS Frontend

A387640 A387523(n) is the a(n)-th prime number.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

Formula

A387524 Primes p with property that in A386482 they are immediately preceded by 2*p and immediately followed by 3*p.

Views

Author

Keywords

Comments

Crossrefs

Extensions

A387634 Indices k such that s(k) is a prime p, s(k-1) = 2*p, and s(k+1) = 3*p, where s = A386482.

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

Extensions

A387524 Primes p with property that in A386482 they are immediately preceded by 2p and immediately followed by 3p.

A387634 Indices k such that s(k) is a prime p, s(k-1) = 2p, and s(k+1) = 3p, where s = A386482.