A114537 - OEIS

A114537

Dispersion of the primes (an array read by downward antidiagonals).

1, 2, 4, 3, 7, 6, 5, 17, 13, 8, 11, 59, 41, 19, 9, 31, 277, 179, 67, 23, 10, 127, 1787, 1063, 331, 83, 29, 12, 709, 15299, 8527, 2221, 431, 109, 37, 14, 5381, 167449, 87803, 19577, 3001, 599, 157, 43, 15, 52711, 2269733, 1128889, 219613, 27457, 4397, 919, 191, 47

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

A number is prime if and only if it does not lie in Column 1. As a sequence, a permutation of the natural numbers. The fractal sequence of this dispersion is A022447 and the transposition sequence is A114538.

The dispersion of the composite numbers is given at A114577.

REFERENCES

Alexandrov, Lubomir. "On the nonasymptotic prime number distribution." arXiv preprint math/9811096 (1998). (See Appendix.)

Clark Kimberling, "Fractal sequences and interspersions," Ars Combinatoria, 45 (1997) 157-168.

LINKS

Robert G. Wilson v, Table of n, a(n) for n = 1..172

Neil Fernandez, An order of primeness, F(p)

Neil Fernandez, An order of primeness [cached copy, included with permission of the author]

Neil Fernandez, The Exploring Primeness Project

Clark Kimberling, Interspersions and Dispersions.

Clark Kimberling, Interspersions and dispersions, Proceedings of the American Mathematical Society, 117 (1993) 313-321.

Robert G. Wilson v, The Northwest Corner of the Primeness Array (24 x 24).

FORMULA

T(r,1) = A018252(r). T(r,c) = prime(T(r,c-1)), c>1. [R. J. Mathar, Oct 22 2010]

EXAMPLE

Northwest corner of the Primeness array:

1 2 3 5 11 31 127 709 5381 52711 648391

4 7 17 59 277 1787 15299 167449 2269733 37139213 718064159

6 13 41 179 1063 8527 87803 1128889 17624813 326851121 7069067389

8 19 67 331 2221 19577 219613 3042161 50728129 997525853 22742734291

9 23 83 431 3001 27457 318211 4535189 77557187 1559861749 36294260117

10 29 109 599 4397 42043 506683 7474967 131807699 2724711961 64988430769

12 37 157 919 7193 72727 919913 14161729 259336153 5545806481 136395369829

14 43 191 1153 9319 96797 1254739 19734581 368345293 8012791231 200147986693

15 47 211 1297 10631 112129 1471343 23391799 440817757 9672485827 243504973489

16 53 241 1523 12763 137077 1828669 29499439 563167303 12501968177 318083817907

18 61 283 1847 15823 173867 2364361 38790341 751783477 16917026909 435748987787

20 71 353 2381 21179 239489 3338989 56011909 1107276647 25366202179 664090238153

21 73 367 2477 22093 250751 3509299 59053067 1170710369 26887732891 705555301183

22 79 401 2749 24859 285191 4030889 68425619 1367161723 31621854169 835122557939

24 89 461 3259 30133 352007 5054303 87019979 1760768239 41192432219 1099216100167

25 97 509 3637 33967 401519 5823667 101146501 2062666783 48596930311 1305164025929

26 101 547 3943 37217 443419 6478961 113256643 2323114841 55022031709 1484830174901

27 103 563 4091 38833 464939 6816631 119535373 2458721501 58379844161 1579041544637

MAPLE

A114537 := proc(r, c) option remember; if c = 1 then A018252(r) ; else ithprime(procname(r, c-1)) ; end if; end proc: # R. J. Mathar, Oct 22 2010

MATHEMATICA

NonPrime[n_] := FixedPoint[n + PrimePi@# + 1 &, n]; t[n_, k_] := Nest[Prime, NonPrime[n], k]; Table[ t[n - k, k], {n, 0, 9}, {k, n, 0, -1}] // Flatten

(* or to view the table *) Table[t[n, k], {n, 0, 6}, {k, 0, 10}] // TableForm (* Robert G. Wilson v, Dec 26 2005 *)

CROSSREFS

Columns 1-13: A018252, A007821, A049078, A049079, A049080, A049081, A058322, A058324, A058325, A058326, A058327, A058328, A093046.

Rows 1-7: A007097, A057450, A057451, A057452, A057453, A057456, A057457.

Diagonal: A181441.

Cf. A000040, A007821, A114538, A006450.

If the antidiagonals are read in the opposite direction we get A138947.

Sequence in context: A191738 A343647 A218602 * A243349 A266413 A245614

Adjacent sequences: A114534 A114535 A114536 * A114538 A114539 A114540

KEYWORD

nonn,tabl,nice

AUTHOR

Clark Kimberling, Dec 07 2005

STATUS

approved