A032606 -id:A032606 - cp's OEIS frontend

A032605 Prime numbers indexed by lucky numbers.

2, 5, 17, 23, 41, 47, 73, 97, 127, 137, 157, 191, 227, 233, 307, 331, 347, 367, 379, 401, 449, 487, 523, 571, 607, 631, 709, 727, 751, 761, 811, 877, 937, 967, 1009, 1019, 1129, 1171, 1187, 1229, 1259, 1297, 1367, 1409, 1453, 1483, 1489, 1523

Offset: 1

Patrick De Geest, May 15 1998

nonn

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

Cf. A000040, A000959, A032606.

A032605 = Range[1, 275, 2]; i = 2; While[i <= (len = Length@A032605) && (k = A032605[[i]]) <= len, A032605 = Drop[A032605, {k, len, k}]; i++ ]; Prime /@ A032605 (* Robert G. Wilson v, May 12 2006 *)

use ntheory ":all"; say "$ ", nth_prime(nth_lucky($)) for 1..20'; # Dana Jacobsen, Dec 21 2018

a(n) = A000040(A000959(n)). - Amiram Eldar, Nov 16 2019

A307009 Numbers that are both lucky-indexed primes and prime-indexed lucky numbers.

Original entry on oeis.org

367, 487, 3499, 5503, 11677, 15187, 15661, 20359, 27091, 31723, 36529, 43669, 60631, 62047, 70783, 72493, 74101, 78487, 93139, 94789, 105529, 123619, 128257, 148249, 164377, 191491, 192931, 210739, 240379, 242413, 271501, 276343, 282589, 290119, 299107

Offset: 1

Amiram Eldar, Mar 19 2019

nonn

Intersection of A032605 and A032606.

Cf. A032605, A032606, A307008, A307010.

m = 10^4; L = Table[2*i + 1, {i, 0, m}]; For[n = 2, n < Length[L], r = L[[n++]]; L = ReplacePart[L, Table[r*i -> Nothing, {i, 1, Length[L]/r}]]]; P = Select[ Range[2m], PrimeQ]; lp = L[[Select[P, # <= Length[L] &]]]; pl = P[[Select[L, # <= Length[P] &]]]; Intersection[lp, pl] (* after Jean-François Alcover at A000959 *)

A307010 Numbers that are prime-indexed primes, lucky-indexed lucky numbers, lucky-indexed primes and prime-indexed lucky numbers.

Original entry on oeis.org

367, 687331, 1983913, 2278033, 2400793, 2760361, 3531247, 5840767, 9429223, 11894593, 13201483, 13371751, 13597357, 13755361, 19782127, 24772663, 25607341, 34723783, 51279127, 56208967, 59215327, 71039257, 74498731, 83170537, 97983187, 109510909, 124762969

Offset: 1

Amiram Eldar, Mar 19 2019

nonn

Intersection of A006450, A032639, A032605 and A032606.

Intersection of A307008 and A307009.

Cf. A006450, A031157, A032605, A032606, A032639, A307008, A307009.

m = 10^4; L = Table[2*i + 1, {i, 0, m}]; For[n = 2, n < Length[L], r = L[[n++]]; L = ReplacePart[L, Table[r*i -> Nothing, {i, 1, Length[L]/r}]]]; P = Select[ Range[2m], PrimeQ]; lp = L[[Select[P, # <= Length[L] &]]]; pl = P[[Select[L, # <= Length[P] &]]]; pp = P[[Select[P, # <= Length[P] &]]]; ll = L[[Select[L, # <= Length[L] &]]]; Intersection[lp, pl, pp, ll] (* after Jean-François Alcover at A000959 *)

A128886 a(n) = prime(lucky(n)) - lucky(prime(n)).

Original entry on oeis.org

-1, -2, 4, 2, 4, -2, 4, 22, 28, 4, 16, 2, 22, 14, 70, 48, 28, 40, 12, 2, 34, 24, 36, 42, 24, 16, 88, 82, 96, 68, 10, 46, 52, 70, 30, 28, 106, 84, 82, 62, 56, 78, 82, 106, 114, 118, 18, -40, 52, 66, 68, 52, 136, 70, 46, 52, 54, 64, 112, 78, 114, 94, 10, 50, 82, 82, 4, 136, 90, 74

Offset: 1

Jonathan Vos Post, May 08 2007

Commutator [prime,lucky] = [A032605, A032606].

			a(1) = Prime(Lucky(1)) - Lucky(Prime(1)) = Prime(1) - Lucky(2) = 2 - 3 = -1.
a(2) = Prime(Lucky(2)) - Lucky(Prime(2)) = Prime(3) - Lucky(3) = 5 - 7 = -2.
a(3) = Prime(Lucky(3)) - Lucky(Prime(3)) = Prime(7) - Lucky(5) = 17 - 13 = 4.

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

Cf. A000040, A000959, A032605 (Prime numbers indexed by lucky numbers), A032606 (Lucky numbers indexed by prime numbers).

use ntheory ":all"; say "$ ", nth_prime(nth_lucky($))-nth_lucky(nth_prime($)) for 1..20; # _Dana Jacobsen, Dec 21 2018

a(n) = A000040(A000959(n)) - A000959(A000040(n)).

Entries corrected starting at a(10) by R. J. Mathar, Oct 22 2010

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A032605 Prime numbers indexed by lucky numbers.

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A307009 Numbers that are both lucky-indexed primes and prime-indexed lucky numbers.

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A307010 Numbers that are prime-indexed primes, lucky-indexed lucky numbers, lucky-indexed primes and prime-indexed lucky numbers.

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A128886 a(n) = prime(lucky(n)) - lucky(prime(n)).

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