A093945 -id:A093945 - cp's OEIS frontend

A107666 Primes having only {4, 6, 9} as digits.

449, 499, 4649, 4969, 4999, 6449, 6469, 6949, 9649, 9949, 44449, 44699, 46499, 46649, 49499, 49669, 49999, 64499, 64969, 66449, 66499, 66949, 69499, 94649, 94949, 94999, 96469, 99469, 444449, 444469, 444649, 446969, 449699, 464699, 464999, 466649, 469649, 469969

Offset: 1

Rick L. Shepherd, May 19 2005

Intersection of A000040 and A107665. - K. D. Bajpai, Sep 08 2014

			From _K. D. Bajpai_, Sep 08 2014: (Start)
4649 is a term because it is a prime having only semiprime digits 4, 6 and 9.
6469 is a term because it is a prime having only semiprime digits 4, 6 and 9.
449 is the smallest prime comprising only semiprime digits 4, 6 or 9.
(End)

Jason Bard, Table of n, a(n) for n = 1..10000 (first 2069 terms from K. D. Bajpai)
Index to entries for primes with digits in a given set

Cf. A107665 (numbers with semiprime digits), A001358 (semiprimes), A051416 (primes whose digits are all composite), A020466 (primes with digits 4 and 9 only), A093402 (primes of form 44...9), A093945 (primes of form 499...).
Cf. A107342, A111494, A111496, A111697.
Cf. A385768 - A385800.

N:= 4:  Dgts:= {4, 6, 9}:  A:= NULL:
for d from 1 to N do
K:= combinat[cartprod]([Dgts minus {0}, Dgts $(d-1)]);
while not K[finished] do L:= K[nextvalue]();  x:= add(L[i]*10^(d-i), i=1..d);
if isprime(x) then A:= A, x fi od od: A;  # K. D. Bajpai, Sep 08 2014

Select[Prime[Range[50000]], Intersection[IntegerDigits[#], {0, 1, 2, 3, 5, 7, 8}] == {} &] (* K. D. Bajpai, Sep 08 2014 *)

a(35)-a(38) from K. D. Bajpai, Sep 08 2014

A067206 Numbers n such that the digits of n end in phi(n).

Original entry on oeis.org

1, 1320, 1640, 1768, 1996, 2640, 3960, 13200, 16400, 19984, 19996, 26400, 39600, 132000, 164000, 199996, 264000, 396000, 1320000, 1640000, 1999936, 2640000, 3960000, 13200000, 16400000, 16666240, 17999488, 18515584, 19999984, 19999996

Offset: 1

Joseph L. Pe, Feb 19 2002

Comments from Farideh Firoozbakht, Dec 30 2006: (Start)
"(1). If n is in the sequence and 10 divides n then for each natural number k, n*10^k is in the sequence. So since 1320, 1640, 2640, 3960 & 16666240 are in the sequence, for each natural number k, 132*10^k, 164*10^k, 264*10^k, 396*10^k & 1666624*10^k are in the sequence. Hence the sequence is infinite.
"(2). If 5*10^k-1 is prime then 4*(5*10^k-1) is in the sequence. So 4*A093945 is a subsequence of this sequence.
"(3). If p=125*10^k-1 is prime then 16*p is in the sequence. For k = 1, 4, 5, 8, 13, 19, 25, 26, 76, 88, 167, 290, 389, ... p is prime.
"(4). If p=3125*10^k-1 is prime then 64*p is in the sequence. For k = 1, 3, 9, 33, 121, 223, 357, 363, 447, ... p is prime." (End)

			The digits of 1768 end in phi(1768) = 768, so 1768 is a term of the sequence.

Pickover, C. "Wonders of Numbers". Oxford Univ. Press, 2001.

Giovanni Resta, Table of n, a(n) for n = 1..66 (terms < 10^12, first 33 terms from Farideh Firoozbakht)
C. A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Zentralblatt review

Cf. A093945, A091439.

Cf. A066663. - R. J. Mathar, Sep 30 2008

(*returns true if a ends in b, false o.w.*) 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]; Select[Range[10^5], f[ #, EulerPhi[ # ]] &]

More terms from Farideh Firoozbakht, Dec 30 2006

A295988 Numbers k such that (10^k)/2 - 1 is prime.

Original entry on oeis.org

3, 4, 5, 7, 15, 55, 211, 391, 595, 3461, 5029, 5220, 5333, 8073, 15797, 16132, 21457, 29283, 78791, 85143, 179973, 211030, 445774, 464844, 511057

Offset: 1

Patrick A. Thomas, Dec 02 2017

			499, 4999, 49999, 4999999 are prime, while 4, 49, 499999, 49999999 are composite.

Cf. A056712, A093945.

Select[Range[10^3], PrimeQ[10^#/2 - 1] &] (* Michael De Vlieger, Dec 02 2017 *)

isok(n) = isprime(10^n/2 - 1); \\ Michel Marcus, Dec 02 2017

a(n) = 1 + A056712(n). - Omar E. Pol, Dec 02 2017

a(7)-a(25) from Michel Marcus and Omar E. Pol, Dec 02 2017

cp's OEIS Frontend

A107666 Primes having only {4, 6, 9} as digits.

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A067206 Numbers n such that the digits of n end in phi(n).

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A295988 Numbers k such that (10^k)/2 - 1 is prime.

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