A046883
Automorphic primes: primes p such that p is k-th prime and p ends in k.
Original entry on oeis.org
17, 99551, 4303027, 6440999, 14968819, 95517973, 527737957, 1893230839, 1246492090901, 12426836115943, 21732382677641, 154895576080181, 2677628540590583, 133475456543097857, 820396537622790811
Offset: 1
p(7)=17, p(9551)=99551, p(303027)=4303027, p(440999)=6440999, p(968819)=14968819, p(5517973)=95517973.
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Do[ If[ Mod[ Prime[n], 10^Ceiling[ Log[10, n]]] == n, Print[Prime[n]]], {n, 1, 100000000, 2}] (* Robert G. Wilson v, May 21 2004 *) (* fixed by Ivan N. Ianakiev, Apr 15 2022 *)
fQ[n_]:=StringPosition[ToString[Prime[n]],ToString[n]][[1,2]]==
IntegerLength[Prime[n]]; Prime[Select[Range[1,5517973,2],fQ]]//Quiet (* Ivan N. Ianakiev, Apr 15 2022 *)
Select[Table[{n,Prime[n]},{n,552*10^4}],Mod[#[[2]],10^IntegerLength[#[[1]]]]==#[[1]]&][[;;,2]] (* The program generates the first six terms of the sequence. *) (* Harvey P. Dale, Mar 18 2025 *)
A067248
Numbers k such that the digits of prime(k) end in k.
Original entry on oeis.org
7, 9551, 303027, 440999, 968819, 5517973, 27737957, 93230839, 46492090901, 426836115943, 732382677641, 4895576080181, 77628540590583, 3475456543097857, 20396537622790811
Offset: 1
Prime(968819) = 14968819 which ends in 968819, so 968819 is a term of the sequence.
Corresponding primes are in
A046883.
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(* returns true if a ends with b, false otherwise *) f[a_, b_] := Module[{c, d, e, g, h, i, r}, r = False; c = ToString[a]; d = ToString[b]; e = StringLength[c]; g = StringPosition[c, d]; h = Length[g]; If[h > 0, i = g[[h]]; If[i[[2]] == e, r = True]]; r]; Do[If[f[Prime[n], n], Print[n]], {n, 1, 10^6}]
A068575
Numbers n such that, as strings, n is a substring of prime(n).
Original entry on oeis.org
7, 6455, 6456, 6457, 6459, 6460, 6466, 9551, 303027, 440999, 968819, 5517973, 27737957, 93230839, 96664044, 46492090901
Offset: 1
Treated as strings, 6455 is a substring of 64553 = Prime(6455), so 6455 belongs to the sequence.
Pairs {n, prime(n)}: {7, 17}, {6455, 64553}, {6456, 64567}, {6457, 64577}, {6459, 64591}, {6460, 64601}, {6466, 64661}, {9551, 99551}, {303027, 4303027}, {440999, 6440999}, {968819, 14968819}, {5517973, 95517973}.
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Select[Range[10^6], StringPosition[ToString[Prime[ # ]], ToString[ # ]] != {} &]
Select[Range[97*10^4],SequenceCount[IntegerDigits[Prime[#]],IntegerDigits[#]]>0&] (* The program generates the first 11 terms of the sequence. *) (* Harvey P. Dale, Nov 14 2022 *)
A103174
Numbers k with increasing digits such that the digits of k appear among the digits of the k-th prime number.
Original entry on oeis.org
7, 5789, 234567, 345679
Offset: 1
n: {7, 5789, 234567, 345679}
prime(n): {17, 57089, 3264857, 4956733}
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Select[Rest@ Union[FromDigits /@ Subsets@ Range@ 9], SubsetQ @@ IntegerDigits@ {Prime@#, #} &] (* Giovanni Resta, Apr 29 2017 *)
A236469
Primes p such that pi(p) = floor(p/10), where pi is the prime counting function.
Original entry on oeis.org
64553, 64567, 64577, 64591, 64601, 64661
Offset: 1
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KD := proc() local a,b; a:=ithprime(n); b:=floor(a/10); if n=b then RETURN (a);fi; end: seq(KD(), n=1..1000000);
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Do[p = Prime[n]; k = Floor[p/10]; If[k == n, Print[p]], {n, 10^6}] (* Bajpai *)
Select[Prime[Range[6500]], PrimePi[#] == Floor[#/10] &] (* Alonso del Arte, Jan 26 2014 *)
Showing 1-5 of 5 results.
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