This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A039993 Number of different primes embedded in n. 17
 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 3, 1, 1, 1, 3, 0, 1, 1, 1, 1, 3, 1, 2, 1, 2, 1, 2, 1, 3, 3, 1, 2, 3, 1, 4, 2, 1, 0, 1, 1, 2, 0, 1, 0, 2, 0, 0, 1, 1, 2, 3, 1, 1, 1, 2, 1, 2, 0, 1, 1, 1, 0, 1, 0, 2, 0, 0, 1, 3, 2, 4, 2, 2, 2, 1, 1, 3, 0, 0, 1, 2, 0, 1, 0, 1, 0, 1, 0, 1, 2, 1, 0, 2, 0, 3, 1, 0, 0, 2, 1, 4, 2, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,13 COMMENTS a(n) counts (distinct) permuted subsequences of digits of n which denote primes. LINKS T. D. Noe, Table of n, a(n) for n=1..10000 C. K. Caldwell, The Prime Glossary, Primeval Number J. P. Delahaye, Primes Hunters, 1379 is very primeval (in French) [broken link] M. Keith, Integers containing many embedded primes W. Schneider, Primeval Numbers G. Villemin's Almanach of Numbers, Mike Keith's Primeval Number (in French). EXAMPLE a(17) = 3 since we can obtain 7, 17 and 71. a(22) = 1, since we can get only one prime (in contrast, A075053(22) = 2). a(1013) = 14 because the prime subsets derived from the digital permutations of 1013 are {3, 11, 13, 31, 101, 103, 113, 131, 311, 1013, 1031, 1103, 1301, 3011}. MATHEMATICA Needs["DiscreteMath`Combinatorica`"]; f[n_] := Block[{a = Drop[ Sort[ Subsets[ IntegerDigits[n]]], 1], b = c = {}, k = 1, l}, l = Length[a] + 1; While[k < l, b = Append[b, Permutations[ a[[k]] ]]; k++ ]; b = Union[ Flatten[b, 1]]; l = Length[b] + 1; k = 1; While[k < l, c = Append[c, FromDigits[ b[[k]] ]]; k++ ]; Count[ PrimeQ[ Union[c]], True]]; Table[ f[n], {n, 1, 105}] Table[Count[Union[FromDigits/@(Flatten[Permutations/@Subsets[ IntegerDigits[ n]], 1])], _?PrimeQ], {n, 110}] (* Harvey P. Dale, Nov 29 2017 *) PROG (PARI) A039993(n)={my(S=[], D=vecsort(digits(n))); for(i=1, 2^#D-1, forperm(vecextract(D, i), p, isprime(fromdigits(Vec(p)))||next; S=setunion(S, [fromdigits(Vec(p))]))); #S} \\ To avoid duplicate scan of identical subsets of digits, one could skip the corresponding range of indices i when a binary pattern ...10... is detected. - M. F. Hasler, Mar 08 2014, simplified Oct 15 2019 (Python) from itertools import permutations from sympy import isprime def a(n):     l=list(str(n))     L=[] for i in range(len(l)): L+=[int("".join(x)) for x in list(permutations(l, i + 1))]     return len(list(filter(lambda i: isprime(i), list(set(L))))) print [a(n) for n in range(1, 101)] # Indranil Ghosh, Jun 25 2017 CROSSREFS Different from A075053. For records see A072857, A076497. See also A134596, A134597. Cf. A039999. Sequence in context: A329210 A325669 A068153 * A075053 A007362 A214709 Adjacent sequences:  A039990 A039991 A039992 * A039994 A039995 A039996 KEYWORD nonn,base,changed AUTHOR EXTENSIONS Edited by Robert G. Wilson v, Nov 25 2002 Keith link repaired by Charles R Greathouse IV, Aug 13 2009 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 14 17:55 EST 2019. Contains 329979 sequences. (Running on oeis4.)