A185641 Least k such that A098591(k) = n or 0 if no such k exists.

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

Offset: 0

Author

Michel Marcus, Jan 31 2013

Keywords

• nonn
• fini
• full

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.

Examples

			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.
		

Links

• Michel Marcus, Table of n, a(n) for n = 0..255
• Phil Carmody, 7 primes in intervals [k*30,(k+1)*30], thread in newsgroup sci.math, Sep 19 2004.
• Hugo Pfoertner, Patterns count table

Crossrefs

Cf. A098591.

Programs

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}] (* Jean-François Alcover, Jan 31 2013 *)