A082122
Smallest difference > 1 between d and p/d for any divisor d of the partial product p of the sequence, starting with 11.
Original entry on oeis.org
11, 10, 17, 21, 23, 31, 43, 167, 6383, 31741, 52112213, 37549127743, 36777947021270771, 504837176634758950812127
Offset: 0
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p=11; print1(p, ", "); for(n=1, 50, v=divisors(p); r=sqrt(p); t=0; for(k=1, matsize(v)[2], if(v[k]>=r, t=k; break)); if(v[t]^2==p, u=t, u=t-1); if(v[t]-v[u]<2, u=u-1; t=t+1); print1(v[t]-v[u]", "); p=p*(v[t]-v[u]))
A082124
Smallest difference>1 between d and p/d for any divisor d of the partial product p of the sequence, starting with 9.
Original entry on oeis.org
9, 8, 6, 6, 6, 36, 39, 618, 4932, 60192, 3075084, 349550100, 15219084556800, 13331385308976969710
Offset: 1
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p=9; print1(p, ", "); for(n=1, 50, v=divisors(p); r=sqrt(p); t=0; for(k=1, matsize(v)[2], if(v[k]>=r, t=k; break)); if(v[t]^2==p, u=t, u=t-1); if(v[t]-v[u]<2, u=u-1; t=t+1); print1(v[t]-v[u]", "); p=p*(v[t]-v[u]))
a(14) from Herman Jamke (hermanjamke(AT)fastmail.fm), Nov 02 2006
A063269
a(1) = 3, a(n) = concatenation of two closest factors of a(n-1) whose product equals a(n-1) or if a(n-1) is a prime then the concatenation of 1 and a(n-1).
Original entry on oeis.org
3, 13, 113, 1113, 2153, 12153, 34051, 172003, 1311313, 3473779, 5365543, 16913173, 34014973, 229148537, 479347809, 1807726517, 11807726517, 20529575173, 69833293981, 179443389167, 230839777353, 376946592451
Offset: 1
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f[ n_Integer ] := (d = Divisors[ n ]; l = Length[ d ]; If[ EvenQ[ l ], ToExpression[ ToString[ d[ [ l/2 ] ] ] <> ToString[ d[ [ l/2 + 1 ] ] ] ], ToExpression[ ToString[ d[ [ l/2 + .5 ] ] ] <> ToString[ d[ [ l/2 + .5 ] ] ] ] ] ); NestList[ f, 3, 24 ]
A063380
a(1) = 4, a(n) = concatenation of two closest factors of a(n-1) whose product equals a(n-1) or if a(n-1) is a prime then the concatenation of 1 and a(n-1).
Original entry on oeis.org
4, 22, 211, 1211, 7173, 9797, 97101, 910789, 1182799, 1319029, 6719687, 7678761, 32559587, 257126691, 1591617149, 6653239233, 62767105999, 126149775659, 432933715713, 2435717774509, 6598336914323, 19495633384521
Offset: 1
-
f[ n_Integer ] := (d = Divisors[ n ]; l = Length[ d ]; If[ EvenQ[ l ], ToExpression[ ToString[ d[ [ l/2 ] ] ] <> ToString[ d[ [ l/2 + 1 ] ] ] ], ToExpression[ ToString[ d[ [ l/2 + .5 ] ] ] <> ToString[ d[ [ l/2 + .5 ] ] ] ] ] ); NestList[ f, 4, 24 ]
A063382
a(1) = 5, a(n) = concatenation of two closest factors of a(n-1) whose product equals a(n-1) or if a(n-1) is a prime then the concatenation of 1 and a(n-1).
Original entry on oeis.org
5, 15, 35, 57, 319, 1129, 11129, 31359, 310453, 1691837, 7241691, 15094799, 31486929, 159198031, 1159198031, 6203186877, 11721529237, 88429132553, 129487682919, 1228291054211, 1394483927247, 8800411584567, 34329256355023
Offset: 1
-
f[ n_Integer ] := (d = Divisors[ n ]; l = Length[ d ]; If[ EvenQ[ l ], ToExpression[ ToString[ d[ [ l/2 ] ] ] <> ToString[ d[ [ l/2 + 1 ] ] ] ], ToExpression[ ToString[ d[ [ l/2 + .5 ] ] ] <> ToString[ d[ [ l/2 + .5 ] ] ] ] ] ); NestList[ f, 5, 24 ]
A063384
a(1) = 7, a(n) = concatenation of two closest factors of a(n-1) whose product equals a(n-1) or if a(n-1) is a prime then the concatenation of 1 and a(n-1).
Original entry on oeis.org
7, 17, 117, 913, 1183, 1391, 13107, 51257, 151257, 381397, 577661, 4911789, 29116879, 112646989, 536920981, 1928258999, 11928258999, 25227472837, 46275452231, 212892173679, 370964057893, 1859199550327, 5593332415439
Offset: 1
-
f[ n_Integer ] := (d = Divisors[ n ]; l = Length[ d ]; If[ EvenQ[ l ], ToExpression[ ToString[ d[[ l/2 ] ]] <> ToString[ d[[ l/2 + 1 ]] ]], ToExpression[ ToString[ d[[ l/2 + .5 ] ]] <> ToString[ d[[ l/2 + .5 ] ]] ]] ); NestList[ f, 7, 25 ]
A063403
a(1) = 8, a(n) = concatenation of two closest factors of a(n-1) whose product equals a(n-1) or if a(n-1) is a prime then the concatenation of 1 and a(n-1).
Original entry on oeis.org
8, 24, 46, 223, 1223, 11223, 87129, 189461, 414621, 2072003, 12072003, 34024001, 163920759, 354640253, 1074732999, 7377145687, 17377145687, 57053304579, 393145173803, 834736688841, 8062231035367, 26899299722333, 27745499695017
Offset: 1
-
f[ n_Integer ] := (d = Divisors[ n ]; l = Length[ d ]; If[ EvenQ[ l ], ToExpression[ ToString[ d[[ l/2 ] ]] <> ToString[ d[[ l/2 + 1 ]] ]], ToExpression[ ToString[ d[[ l/2 + .5 ] ]] <> ToString[ d[[ l/2 + .5 ] ]] ]] ); NestList[ f, 8, 25 ]
A063423
a(1) = 9, a(n) = concatenation of two closest factors of a(n-1) whose product equals a(n-1) or if a(n-1) is a prime then the concatenation of 1 and a(n-1).
Original entry on oeis.org
9, 33, 311, 1311, 2357, 12357, 91373, 191373, 273701, 594639, 966071, 3792549, 7714919, 18474177, 36158059, 217166627, 415296747, 1269327263, 8581147923, 85531003291, 307572780863, 417501775143, 594709702027, 1334471501519
Offset: 1
-
f[ n_Integer ] := (d = Divisors[ n ]; l = Length[ d ]; If[ EvenQ[ l ], ToExpression[ ToString[ d[ [ l/2 ] ] ] <> ToString[ d[ [ l/2 + 1 ] ] ] ], ToExpression[ ToString[ d[ [ l/2 + .5 ] ] ] <> ToString[ d[ [ l/2 + .5 ] ] ] ] ] ); NestList[ f, 9, 25 ]
A063424
a(1) = 10, a(n) = concatenation of two closest factors of a(n-1) whose product equals a(n-1) or if a(n-1) is a prime then the concatenation of 1 and a(n-1).
Original entry on oeis.org
10, 25, 55, 511, 773, 1773, 9197, 17541, 91949, 143643, 347881, 3311051, 13311051, 35433757, 71499067, 72619847, 74179791, 82678973, 613313481, 1551395431, 1679289793, 4339053251, 6529966449, 9370214693, 71338602099, 222407320757
Offset: 1
-
f[ n_Integer ] := (d = Divisors[ n ]; l = Length[ d ]; If[ EvenQ[ l ], ToExpression[ ToString[ d[ [ l/2 ] ] ] <> ToString[ d[ [ l/2 + 1 ] ] ] ], ToExpression[ ToString[ d[ [ l/2 + .5 ] ] ] <> ToString[ d[ [ l/2 + .5 ] ] ] ] ] ); NestList[ f, 10, 25 ]
A246463
a(n) = min(p +- q) > 1 with p*q being equal to the n-th primorial (A002110).
Original entry on oeis.org
5, 7, 11, 13, 17, 107, 41, 157, 1811, 1579, 18859, 95533, 17659, 1995293, 208303, 2396687, 58513111, 299808329, 3952306763, 341777053, 115405393057, 437621467859, 1009861675153, 6660853109087, 29075165225531, 418895584426457, 2371362636817019, 6889206780487667, 5258351738694673
Offset: 2
a(7) = 41 since the middle four divisors of 7# or 2*3*5*7*11*13*17 = 510510 are 663, 714, 715 and 770. Because the middle two only differ by 1, the next pair, 663 and 770 are used and their difference is 107.
a(8) = 41 since the middle two divisors of 8# are 3094 and 3135 which have a difference of 41.
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f[n_] := Block[{k = mx = 1, fi = Prime@ Range@ n, prod = Fold[Times, 1, Prime@ Range@ n], sqrt, tms}, sqrt = Floor@ Sqrt@ prod; While[k < 2^n, tms = Times @@ (fi^IntegerDigits[k, 2, n]); If[mx < tms < sqrt, mx = tms]; k++]; prod/mx - mx]; Array[f, 30, 2]
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a(n)=my(P=prod(i=1,n,prime(i)));forstep(k=sqrtint(P),1,-1,if(P%k==0 && P/k-k>1, return(P/k-k))) \\ Charles R Greathouse IV, Aug 31 2014
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a(n)=my(P=prod(i=1,n,prime(i)),t); fordiv(P,d, if(P/d-d>1, t=P/d-d, return(t))) \\ Charles R Greathouse IV, Aug 31 2014
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