

A185641


Least k such that A098591(k) = n or 0 if no such k exists.


3



360, 161, 139, 44, 655, 186, 178, 184, 83, 265, 296, 153, 17, 464, 405, 485, 271, 61, 452, 54, 199, 190, 230, 78, 224, 131, 82, 355, 122, 372, 10, 2689, 528, 72, 173, 277, 116, 331, 101, 207, 632, 303, 37, 58, 136, 35, 48, 181, 151, 390, 243, 118, 237, 973
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OFFSET

0,1


COMMENTS

Phil Carmody observed "7 must divide at least one of the terms. That's why (apart from the excluded k=0 range) only <=7 of the 8 terms can be prime. If 7 divides 30*k+1, it also divides 30*k+1+4*7." (See sci.math link.)
a(n)=0 for n = 127, 254 and 255.
The maximum value for a(n) is obtained for a(247)=22621.


LINKS

Michel Marcus, Table of n, a(n) for n = 0..255
Phil Carmody, 7 primes in intervals [k*30,(k+1)*30] thread
Hugo Pfoertner, Patterns count table


EXAMPLE

a(0) = 360, because A098591(360) = 0 is the first occurrence of a 0 in A098591, indicating that there are no primes between 360*30 = 10800 and 10830, i.e., 10800 + {1,7,11,13,17,19,23,29} are composite.


MATHEMATICA

max = 10^5; A098591[n_] := Sum[ 2^k*Boole[ PrimeQ[ 30*n + {1, 7, 11, 13, 17, 19, 23, 29}[[k+1]] ] ], {k, 0, 7}]; a[n_] := Catch[ For[ k = 1, k <= max, k++, If[ A098591[k] == n, Throw[k], If[ k >= max, Throw[0]]]]]; Table[ Print[n, " ", an = a[n]]; an, {n, 0, 255}] (* JeanFrançois Alcover, Jan 31 2013 *)


CROSSREFS

Cf. A098591.
Sequence in context: A101996 A237017 A097570 * A031966 A137487 A069478
Adjacent sequences: A185638 A185639 A185640 * A185642 A185643 A185644


KEYWORD

nonn,fini,full


AUTHOR

Michel Marcus, Jan 31 2013


STATUS

approved



