Échange virgule contre chiffre-à-gauche

S =

21,12,32,91,33,1,72,111,92,231,132,272,291,273,14,15,4,34,74,192,332,391,312,411,371,392,511,492,572,632,692,711,512,771,

573,75,35,93,112,812,831,633,133,171,671,731,791,813,314,212,931,912,1111,932,1131,972,1292,1311,992,1371,1032,1411,1092,

1431,1172,1532,1611,1232,1791,1293,372,2031,1512,2071,1533,471,1631,1711,1812,2132,2211,1872,2372,2391,1932,2431,2012,2511,

2133,493,531,2171,2231,2291,2312,2672,2691,2373,591,...

P =

2,11,23,29,13,3,17,211,19,223,113,227,229,127,31,41,5,43,47,419,233,239,131,241,137,139,251,149,257,263,269,271,151,277,

157,37,53,59,311,281,283,163,313,317,167,173,179,181,331,421,293,191,2111,193,2113,197,2129,2131,199,2137,1103,2141,1109,

2143,1117,2153,2161,1123,2179,1129,337,2203,1151,2207,1153,347,1163,1171,1181,2213,2221,1187,2237,2239,1193,2243,1201,2251,

1213,349,353,1217,1223,1229,1231,2267,2269,1237,359,1...

En poussant toutes les virgules de S d'un cran vers la gauche on transforme une suite S de non-premiers (tous différents les uns des autres) en une suite P de premiers (tous différents les uns des autres).

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[Maximilian Hasler] :

That was easy (after recognizing that S(n) must not end in "0" ;-).

I find the same terms as you (I think - cf. below).

Maximilian

{used=0;S=[]; for(n=1,99, for(s=1,1e9, bittest(used,s) & next;

isprime(s) & next; s%10|next;

p=eval(Str(if(n>0,S[n]%10,""),if(s>9,s\10,""))); bittest(used,p) &

next; isprime(p) | next;

print(n"\t"s"\t"p);S=concat(S,s);used+=2^s+2^p;break));S}

n n-p p

1 21 2

2 12 11

3 32 23

4 91 29

5 33 13

6 1 3

7 72 17

8 111 211

9 92 19

10 231 223

11 132 113

12 272 227

13 291 229

14 273 127

15 14 31

16 15 41

17 4 5

18 34 43

19 74 47

20 192 419

21 332 233

22 391 239

23 312 131

24 411 241

25 371 137

26 392 139

27 511 251

28 492 149

29 572 257

30 632 263

31 692 269

32 711 271

33 512 151

34 771 277

35 573 157

36 75 37

37 35 53

38 93 59

39 112 311

40 812 281

41 831 283

42 633 163

43 133 313

44 171 317

45 671 167

46 731 173

47 791 179

48 813 181

49 314 331

50 212 421

51 931 293

52 912 191

53 1111 2111

54 932 193

55 1131 2113

56 972 197

57 1292 2129

58 1311 2131

59 992 199

60 1371 2137

61 1032 1103

62 1411 2141

63 1092 1109

64 1431 2143

65 1172 1117

66 1532 2153

67 1611 2161

68 1232 1123

69 1791 2179

70 1293 1129

71 372 337

72 2031 2203

73 1512 1151

74 2071 2207

75 1533 1153

76 471 347

77 1631 1163

78 1711 1171

79 1812 1181

80 2132 2213

81 2211 2221

82 1872 1187

83 2372 2237

84 2391 2239

85 1932 1193

86 2431 2243

87 2012 1201

88 2511 2251

89 2133 1213

90 493 349

91 531 353

92 2171 1217

93 2231 1223

94 2291 1229

95 2312 1231

96 2672 2267

97 2691 2269

98 2373 1237

99 591 359

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[Graeme McRae] :

In base 2, the sequences are

P=7,29,59,79,113,131,137,149,...

S=15,27,55,95,99,135,147,171,...

In base 3,

P=2,7,13,23,17,19,29,41,67,43,...

S=8,4,14,16,25,32,34,44,40,49,...

--Graeme McRae, Palmdale, CA.