A073324 Smallest x such that prime(x) mod c(x) = n, where prime(j) is the j-th prime, c(j) is the j-th composite number.

5, 1, 2, 8, 3, 242, 4, 245, 100, 8313, 10, 50190, 23, 8338, 3390, 12, 24, 308926, 13, 49, 25, 15, 26, 12556637, 112, 55, 117, 58, 56, 1400, 59, 265, 122, 267, 31, 12556641, 603, 270, 33, 12556639, 126, 272, 65, 66, 127, 63, 35, 50270, 37, 1413, 129, 1434, 38, 1411

Offset

1,1

Links

Giovanni Resta, Table of n, a(n) for n = 1..400

Formula

a(n) = Min{x; A000040(x) mod A002808(x) = n} = Min{x; A065859(x) = n}.

Example

x=10: p(10)=29,c(10)=18, Mod[29,18]=11 appears first here, so a(11)=10.

Mathematica

f[x_] := Mod[Prime[x], FixedPoint[x+PrimePi[ # ]+1&, x]] t=Table[0, {256}]; Do[s=f[n]; If[s<257&&t[[s]]==0, t[[s]]=n], {n, 1, 400000}]; t
Module[{nn=500000, cmps, prs, len}, cmps=Select[Range[nn], CompositeQ]; len= Length[ cmps]; Table[SelectFirst[Thread[{Range[len], Prime[Range[len]], cmps}], Mod[#[[2]], #[[3]]] ==n&], {n, 23}]][[All, 1]] (* The program generates the first 23 terms of the sequence. *) (* Harvey P. Dale, Nov 26 2022 *)

Prog

(PARI) isc(n) = (n != 1) && !isprime(n);
lista(nn) = {my(vp = primes(nn), vc = select(x->isc(x), [1..nn])); for (n=1, 50, my(k=1); while((vp[k] % vc[k]) != n, k++; if ((k>#vp) || (k>#vc), return)); print1(k, ", "); ); } \\ Michel Marcus, Sep 02 2019
(PARI) a(n) = my(p=2); forcomposite(c=4, oo, if(p % c == n, return(primepi(p))); p = nextprime(p+1)); \\ Daniel Suteu, Sep 02 2019

Crossrefs

Cf. A000040, A002808, A065859, A073325, A073326.

Sequence in context: A144738 A371849 A021199 * A021665 A226613 A274989

Adjacent sequences: A073321 A073322 A073323 * A073325 A073326 A073327

Keyword

nonn

Author

Labos Elemer, Jul 30 2002

Extensions

a(24)-a(50) from Michel Marcus, Sep 02 2019

More terms from Giovanni Resta, Sep 03 2019

Status

approved