A064425 -id:A064425 - cp's OEIS frontend

A064955 Position of n-th prime in A064413.

2, 5, 10, 14, 20, 28, 33, 37, 43, 57, 61, 67, 74, 81, 89, 100, 107, 115, 128, 134, 138, 151, 160, 167, 182, 189, 197, 203, 207, 216, 236, 253, 259, 264, 279, 287, 297, 305, 314, 328, 336, 344, 363, 371, 377, 381, 401, 420, 430, 438, 444, 458, 462, 474, 487, 501, 510, 517, 530, 540, 549, 557, 581, 587, 599, 606, 629, 639, 655, 664, 670, 681, 699, 707, 724, 730, 736, 756, 766, 781, 798, 802, 814, 819, 833, 848, 857, 874, 882, 889, 898, 911, 927, 942, 953, 961, 971, 997, 1004, 1029, 1041, 1059, 1072, 1080, 1087, 1099, 1118, 1135, 1142, 1150, 1156, 1175, 1181, 1190, 1203, 1223, 1232, 1242, 1249, 1258, 1266, 1287, 1298, 1306, 1324, 1350, 1357, 1378, 1391, 1398, 1410, 1425, 1433, 1442, 1456, 1470, 1478, 1504, 1516, 1542, 1546, 1564, 1568, 1578, 1586, 1610, 1626, 1638, 1646, 1652, 1680, 1686, 1693, 1702, 1734, 1739, 1760

Offset: 1

N. J. A. Sloane, Oct 30 2001

nonn

It can be shown that this sequence is monotonic.

A073734(a(n)) = A000040(n) for n > 1. - Reinhard Zumkeller, Sep 17 2001

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
J. C. Lagarias, E. M. Rains and N. J. A. Sloane, The EKG sequence, Exper. Math. 11 (2002), 437-446.
Index entries for sequences related to EKG sequence

Cf. A000040, A064413, A064425, A064664, A073734.

Setwise difference A383294 \ A383295.

import Data.List (elemIndex)
import Data.Maybe (fromJust)
a064955 n = a064955_list !! (n-1)
a064955_list =
   map ((+ 1) . fromJust . (`elemIndex` a064413_list)) a000040_list
-- Reinhard Zumkeller, Sep 17 2001

ekg[s_] := Block[{m = s[[-1]], k = 3}, While[MemberQ[s, k] || GCD[m, k] == 1, k++]; Append[s, k]];
A064413 = Nest[ekg, {1, 2}, 1000];
Position[A064413, ?PrimeQ] // Flatten (* _Jean-François Alcover, Nov 03 2018, after Robert G. Wilson v in 064413 *)

a(n) = A064664(A000040(n)).

A064423 Position of n-th prime in A064413 (if it begins at 2).

Original entry on oeis.org

1, 4, 9, 13, 19, 27, 32, 36, 42, 56, 60, 66, 73, 80, 88, 99, 106, 114, 127, 133, 137, 150, 159, 166, 181, 188, 196, 202, 206, 215, 235, 252, 258, 263, 278, 286, 296, 304, 313, 327, 335, 343, 362, 370, 376, 380, 400, 419, 429, 437, 443, 457, 461, 473, 486, 500, 509, 516, 529, 539, 548, 556, 580, 586, 598, 605, 628, 638, 654, 663, 669, 680, 698, 706, 723, 729, 735, 755, 765, 780, 797, 801, 813, 818, 832, 847, 856, 873, 881, 888, 897, 910, 926, 941, 952, 960, 970, 996, 1003, 1028, 1040, 1058, 1071, 1079, 1086, 1098, 1117, 1134, 1141, 1149, 1155, 1174, 1180, 1189, 1202, 1222, 1231, 1241, 1248, 1257, 1265, 1286, 1297, 1305, 1323, 1349, 1356, 1377, 1390, 1397, 1409, 1424, 1432, 1441, 1455, 1469, 1477, 1503, 1515, 1541, 1545, 1563, 1567, 1577, 1585, 1609, 1625, 1637, 1645, 1651, 1679, 1685, 1692, 1701, 1733, 1738, 1759

Offset: 1

N. J. A. Sloane, Sep 30 2001

It can be shown that this sequence is monotonic.

T. D. Noe, Table of n, a(n) for n = 1..1000
J. C. Lagarias, E. M. Rains and N. J. A. Sloane, The EKG sequence, arXiv:math/0204011 [math.NT], 2002.
J. C. Lagarias, E. M. Rains and N. J. A. Sloane, The EKG sequence, Exper. Math. 11 (2002), 437-446.
Index entries for sequences related to EKG sequence

Cf. A064413, A064425. See A064955 for better version.

terms = 100;
ekg[s_] := Block[{m = s[[-1]], k = 3}, While[MemberQ[s, k] || GCD[m, k] == 1, k++]; Append[s, k]];
EKG = Nest[ekg, {2, 4}, 12 terms];
a[n_] := FirstPosition[EKG, Prime[n]][[1]];
Array[a, terms] (* Jean-François Alcover, Sep 02 2018, after Robert G. Wilson v in A064413 *)

More terms from Vladeta Jovovic, Oct 01 2001

A137847 Smallest number missing in the EKG sequence (A064413) after n terms.

Original entry on oeis.org

2, 3, 3, 3, 5, 5, 5, 5, 5, 7, 7, 7, 7, 11, 11, 11, 11, 11, 11, 13, 13, 13, 13, 13, 13, 13, 13, 17, 17, 17, 17, 17, 19, 19, 19, 19, 23, 23, 23, 23, 23, 23, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 31, 31, 31, 31, 37, 37, 37, 37, 37, 37, 41, 41, 41, 41, 41, 41, 41, 43

Offset: 1

Zak Seidov, May 12 2008

nonn

Lengths of runs gives A064425 prefixed by a 2.

			a(1)=2 because the least integer absent in EKG with 1 term, {1}, is 2;
a(2..4)=3 because the least integer absent in EKG with 4 terms, {1,2,4,6}, is 3;
a(5..9)=5 because the least integer absent in EKG with 9 terms, {1,2,4,6,3,9,12,8,10}, is 5;
a(10..13)=7 because the least integer absent in EKG with 15 terms, {1,2,4,6,3,9,12,8,10}, is 7.

Index entries for sequences related to EKG sequence

Cf. A064413, A064425.

Entries checked by Jacques Tramu and Vladeta Jovovic.

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A064955 Position of n-th prime in A064413.

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A064423 Position of n-th prime in A064413 (if it begins at 2).

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A137847 Smallest number missing in the EKG sequence (A064413) after n terms.

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