A179675 Smallest m such that the n-th odd prime is the smallest number coprime to m and m+1.

1, 2, 5, 14, 209, 1364, 714, 62985, 367080, 728364, 64822394, 1306238010, 11182598504, 715041747420, 51913478860880, 454746157008780, 9314160363311804, 560934821217378530, 261062105979210899, 696537082207206753590, 54097844397380813592485, 286495021083846822067820, 80126789479717708423427654

Offset: 1

Author

Reinhard Zumkeller, Jul 23 2010; corrected Jul 27 2010

Keywords

• nonn

Comments

A053670(a(n)) = A065091(n) and A053670(m) <> A065091(n) for m < a(n).

Examples

			n=4: a(4) = 14, A065091(4) = A053670(14) = 11,
a(4) = 14 = 2*7, a(4)+1 = 15 = 3*5;
n=5: a(5) = 209, A065091(5) = A053670(209) = 13,
a(5) = 209 = 11*19, a(5)+1 = 210 = 2*3*5*7;
n=6: a(6) = 1364, A065091(6) = A053670(1364) = 17,
a(6) = 1364 = 2*2*11*31, a(6)+1 = 1365 = 3*5*7*13.
a(6) is not 714 even though 714 * 715 is divisible by the first 6 primes. It is disqualified as it is also a multiple of prime(6+1) = 17. - _David A. Corneth_, Aug 16 2023
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..42

Crossrefs

Cf. A053670, A065091.

Programs

Mathematica

With[{s = Table[k = 1; While[! CoprimeQ[n, n + 1, Set[p, Prime@ k]], k++]; p, {n, 10^6}]}, Flatten@ Table[FirstPosition[s, Prime@ n], {n, 2, PrimePi@ Max@ s}]] (* Michael De Vlieger, Aug 01 2017 *)

PARI

a(n) = {my(res = oo, pr = primes(n+1), mp = pr[#pr], mpm1 = mp - 1); v = vector(n, i, [-1, 0]); forvec(x = v, c = lift(chinese(vector(n, i, Mod(x[i], pr[i])))); if(0 < c && c < res, if(c % mp != 0 && c % mp != mpm1, res = c))); res} \\ David A. Corneth, Aug 16 2023

Extensions

a(11)-a(19) from Donovan Johnson, Jul 30 2010

More terms from David A. Corneth, Aug 16 2023