A219785
Primes not neighboring an 11-smooth number.
Original entry on oeis.org
103, 137, 157, 173, 227, 229, 233, 277, 283, 311, 313, 317, 347, 367, 373, 389, 409, 443, 457, 467, 509, 521, 523, 547, 557, 563, 569, 571, 607, 613, 619, 643, 653, 677, 683, 691, 709, 733, 739, 743, 761, 773, 787, 797, 821, 823, 827, 829, 853, 857, 859, 877
Offset: 1
103 is in the sequence because it is prime and the closest 11-smooth numbers are 100 and 105, which differ from 103 by 3 and -2 respectively, neither being -1 or +1.
137 is in the sequence because it is prime and neither 137 - 1 = 136 = 2^3 * 17 nor 137 + 1 = 138 = 2 * 3 * 23 are 11-smooth.
-
mx = 2^10; t11 = Select[Sort[Flatten[Table[2^i 3^j 5^k 7^l 11^m, {i, 0, Log[2, mx]}, {j, 0, Log[3, mx]}, {k, 0, Log[5, mx]}, {l, 0, Log[7, mx]}, {m, 0, Log[11, mx]}]]], # <= mx &]; Complement[Prime[Range[PrimePi[mx]]], Union[Select[t11 + 1, PrimeQ], Select[t11 - 1, PrimeQ]]] (* T. D. Noe, Nov 27 2012 *)
A219790
Smallest prime not neighboring a prime(n)-smooth number.
Original entry on oeis.org
11, 29, 43, 67, 103, 137, 173, 173, 173, 283, 283, 283, 283, 283, 317, 653, 653, 653, 653, 653, 653, 653, 653, 653, 653, 653, 653, 653, 787, 787, 787, 907, 907, 907, 907, 1433, 1433, 1433, 1433, 1433, 1447, 1543, 1543, 1867, 1867, 1867, 1867, 1867, 1867
Offset: 1
a(2) = 29, the smallest prime not neighboring a 3-smooth number, since 3 is the 2nd prime; i.e., not of the form 2^j*3^k +/- 1. 43-1 = 2*3*7, 43+1 = 2*2*11, so neither are 5-smooth.
a(3) = 43, the smallest prime not neighboring a 5-smooth number, since 5 is the 3rd prime, and 43-1 = 42 = 2 * 3 * 7 is not 5 smooth, and 43+1 = 44 = 2^2 * 11 is not 5 smooth. - corrected by _Jason Kimberley_, Nov 29 2012
a(4) = 67, the smallest prime not neighboring a 7-smooth number, since 7 is the 4th prime, and 67-1 = 66 = 2 * 3 * 11 is not 7 smooth, and 67+1 = 68 = 2^2 * 17 is not 7 smooth. - corrected by _Jason Kimberley_, Nov 29 2012
a(5) = 103, the smallest prime not neighboring a 11-smooth number, since 11 is the 5th prime, and 103-1 = 102 = 2 * 3 * 17 is not 11 smooth, and 103+1 = 104 = 2^3 * 13 is not 11 smooth.
a(6) = 137, the smallest prime not neighboring a 13-smooth number, since 13 is the 6th prime, and 137-1 = 136 = 2^3 * 17 is not 13 smooth, and 137+1 = 138 = 2 * 3 * 23 is not 13 smooth.
-
a(n)=my(p=prime(n));forprime(q=6*p-1,,if(vecmax(factor(q-1)[,1])>p && vecmax(factor(q+1)[,1])>p,return(q))) \\ Charles R Greathouse IV, Nov 28 2012
Showing 1-2 of 2 results.