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

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

Author

N. J. A. Sloane, Sep 30 2001

Keywords

• nonn
• nice

Comments

It can be shown that this sequence is monotonic.

Links

• 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

Crossrefs

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

Programs

Mathematica

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 *)

Extensions

More terms from Vladeta Jovovic, Oct 01 2001