A214523
a(1) = 13, a(n) is smallest prime of the form k*a(n-1) + 1.
Original entry on oeis.org
13, 53, 107, 643, 7717, 30869, 432167, 6050339, 12100679, 169409507, 9148113379, 439109442193, 5269313306317, 84309012901073, 7587811161096571, 303512446443862841, 69807862682088453431, 2652698781919361230379, 143245734223645506440467
Offset: 1
53 = 4*13 + 1 ; 107 = 2*53 + 1.
-
t = {13}; Do[k = 1; While[p = k*t[[-1]] + 1; ! PrimeQ[p], k++]; AppendTo[t, p], {20}]; t (* T. D. Noe, Jul 24 2012 *)
nxt[n_]:=Module[{k=1},While[!PrimeQ[k*n+1],k++];n*k+1]; NestList[nxt,13,20] (* Harvey P. Dale, Apr 28 2014 *)
-
a=13;for(n=1,200,b=a*n+1;if(isprime(b),a=b;print1(a,", ");next(n=1)))
A214632
a(1) = 17, a(n) is smallest prime of the form k*a(n - 1) + 1.
Original entry on oeis.org
17, 103, 619, 2477, 34679, 416149, 7490683, 29962733, 419478263, 5872695683, 82217739563, 986612874757, 27625160493197, 994505777755093, 5967034666530559, 71604415998366709, 6444397439853003811, 180443128315884106709, 9743928929057741762287
Offset: 1
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t = {17}; Do[k = 1; While[p = k*t[[-1]] + 1; ! PrimeQ[p], k++]; AppendTo[t, p], {20}]; t (* T. D. Noe, Jul 24 2012 *)
nxt[n_]:=Module[{k=1},While[!PrimeQ[k*n+1],k++];k*n+1]; NestList[nxt,17,20] (* Harvey P. Dale, Apr 18 2014 *)
A214633
a(1)=2; a(n) is smallest prime of the form k*a(n-1) + 3, k>0.
Original entry on oeis.org
2, 5, 13, 29, 61, 491, 3931, 15727, 157273, 314549, 4403689, 17614759, 387524701, 5425345817, 119357607977, 9787323854117, 78298590832939, 1722568998324661, 68902759932986443, 4685387675443078127, 318606361930129312639, 637212723860258625281
Offset: 1
-
A214633 := proc(n)
option remember;
local k;
if n = 1 then
2;
else
for k from 1 do
if isprime(k*procname(n-1)+3) then
return k*procname(n-1)+3 ;
end if;
end do:
end if;
end proc:
seq(A214633(n),n=1..20) ; # R. J. Mathar, Jul 23 2012
A071258
a(1) = 4; a(n) = smallest composite number of form k*a(n-1) + 1 with k > 1.
Original entry on oeis.org
4, 9, 28, 57, 115, 231, 694, 1389, 2779, 5559, 16678, 33357, 66715, 133431, 400294, 800589, 1601179, 3202359, 9607078, 19214157, 38428315, 76856631, 153713263, 307426527, 614853055, 1229706111, 3689118334, 7378236669, 14756473339
Offset: 0
-
nxt[n_]:=Module[{k=2},While[PrimeQ[k*n+1],k++];k*n+1]; NestList[nxt,4,30] (* Harvey P. Dale, Mar 26 2014 *)
A214634
a(1) = 7; a(n) is smallest prime of the form k*a(n-1) + 3, k>0.
Original entry on oeis.org
7, 17, 37, 151, 607, 1217, 2437, 4877, 39019, 78041, 624331, 6243313, 174812767, 1398502139, 19579029949, 39158059901, 1957902995053, 15663223960427, 156632239604273, 3132644792085463, 181693397940956857, 726773591763827431, 7267735917638274313, 1148302274986847341457, 4593209099947389365831
Offset: 1
a(2) = 17 = 2 * 7 + 3.
a(3) = 37 = 2 * 17 + 3.
a(4) = 151 = 4 * 37 + 3.
-
A214634 := proc(n)
option remember;
local k;
if n = 1 then
7;
else
for k from 1 do
if isprime(k*procname(n-1)+3) then
return k*procname(n-1)+3 ;
end if;
end do:
end if;
end proc:
seq(A214634(n),n=1..20) ; # R. J. Mathar, Jul 23 2012
-
spf[n_]:=Module[{k=1},While[!PrimeQ[k*n+3],k++];k*n+3]; NestList[spf,7,25] (* Harvey P. Dale, Aug 02 2017 *)
-
a=7;for(n=1,200,b=a*n+3;if(isprime(b),a=b;print1(a,", ");next(n=1)))
A214680
a(1)=3; a(n) is the smallest prime of the form k*a(n-1) + 2.
Original entry on oeis.org
3, 5, 7, 23, 71, 73, 367, 1103, 7723, 131293, 3807499, 19037497, 57112493, 1427812327, 15705935599, 141353420393, 989473942753, 44526327423887, 311684291967211, 4675264379508167, 4675264379508169, 275840598390981973, 4137608975864729597
Offset: 1
-
t = {3}; Do[k = 1; While[p = k*t[[-1]] + 2; ! PrimeQ[p], k++]; AppendTo[t, p], {25}]; t (* T. D. Noe, Jul 26 2012 *)
Showing 1-6 of 6 results.
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