A236226
Sum of the eighteenth powers of the first n primes.
Original entry on oeis.org
262144, 387682633, 3815084948258, 1632228682858707, 5561549542175090188, 118016956494132483317, 14181101408561857474326, 118308451706473099007167, 3362459361601721384307536, 213819743726773841714612697, 912873363725818880253782938
Offset: 1
Cf.
A085450 = smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n.
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Table[Sum[Prime[k]^18, {k, n}], {n, 1000}]
Accumulate[Prime[Range[20]]^18] (* Harvey P. Dale, Jul 08 2024 *)
A236227
Sum of the nineteenth powers of the first n primes.
Original entry on oeis.org
524288, 1162785755, 19074649113880, 11417969834487023, 61170508418249033314, 1523090798793695143991, 240595526483945019991144, 2219015182144258609115123, 76834486109734969171023610, 6180095732699726458749873279, 27850757952670122653464150750
Offset: 1
Cf.
A085450 = smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n.
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Table[Sum[Prime[k]^19, {k, n}], {n, 1000}]
A232770
Prime(k), where k is such that (Sum_{i=1..k} prime(i)^13) / k is an integer.
Original entry on oeis.org
2, 83, 1979, 2081, 2326469, 6356923, 7170679, 63812027, 4652001719, 241949473277, 163220642765623, 1260677492111911, 8150959175977039
Offset: 1
a(2) = 83, because 83 is the 23rd prime and the sum of the first 23 primes^13 = 17226586990098074754709144 when divided by 23 equals 748982043047742380639528 which is an integer.
Cf.
A085450 (smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n).
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t = {}; sm = 0; Do[sm = sm + Prime[n]^13; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *)
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is(n)=if(!isprime(n),return(0)); my(t=primepi(n),s); forprime(p=2,n,s+=Mod(p,t)^13); s==0 \\ Charles R Greathouse IV, Nov 30 2013
A232848
Prime(k), where k divides Sum_{i=1..k} prime(i)^15.
Original entry on oeis.org
2, 59, 97, 127, 12517, 54581, 83921, 89273, 1396411, 2562719, 4952183, 29201281, 35562101, 47567557, 111213143, 184201627, 1172476337, 7309217299, 287609314877, 5173838081669, 408907258717171, 1357729730868191, 66413899001789557
Offset: 1
a(2) = 59, because 59 is the 17th prime and the sum of the first 17 primes^15 = 455708280934100194626604550 when divided by 17 equals 26806369466711776154506150 which is an integer.
Cf.
A085450 (smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n),
A131275.
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t = {}; sm = 0; Do[sm = sm + Prime[n]^15; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *)
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is(n)=if(!isprime(n),return(0)); my(t=primepi(n),s); forprime(p=2,n,s+=Mod(p,t)^15); s==0 \\ Charles R Greathouse IV, Nov 30 2013
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S=n=0;forprime(p=1,,(S+=p^15)%n++||print1(p",")) \\ M. F. Hasler, Dec 01 2013
A232963
Prime(m), where m is such that (sum_{i=1..m} prime(i)^14) / m is an integer.
Original entry on oeis.org
2, 1933, 3217, 41681, 114311, 2743691233, 7252463461, 28682755720447, 2839633449523319
Offset: 1
a(2) = 1933, because 1193391 is the 295th prime and the sum of the first 295 primes^14 = 172657243368537051859007103457435197295421033550 when divided by 295 equals 585278791079786616471210520194695584052274690 which is an integer.
Cf.
A085450 = smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n.
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t = {}; sm = 0; Do[sm = sm + Prime[n]^14; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *)
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is(n)=if(!isprime(n),return(0)); my(t=primepi(n),s); forprime(p=2,n,s+=Mod(p,t)^14); s==0 \\ Charles R Greathouse IV, Nov 30 2013
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S=n=0;forprime(p=1,,(S+=p^14)%n++||print1(p",")) \\ M. F. Hasler, Dec 01 2013
A233192
Prime(k), where k is such that (Sum_{j=1..k} prime(j)^11) / k is an integer.
Original entry on oeis.org
2, 97, 277, 23311, 61583, 6133811, 210952097, 359643241, 5451597181, 42641466149, 51575229001, 199655689679, 248181386429, 61646670874849, 82153230089767, 212374157550341, 11432141933990629, 15031011453909223
Offset: 1
a(2) = 97, because 97 is the 25th prime and the sum of the first 25 primes^11 = 12718098700540100969050 when divided by 25 equals 508723948021604038762 which is an integer.
Cf.
A085450 = smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n.
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t = {}; sm = 0; Do[sm = sm + Prime[n]^11; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *)
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is(n)=if(!isprime(n),return(0)); my(t=primepi(n),s); forprime(p=2,n,s+=Mod(p,t)^11); s==0 \\ Charles R Greathouse IV, Nov 30 2013
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S=n=0;forprime(p=1,,(S+=p^11)%n++||print1(p",")) \\ M. F. Hasler, Dec 01 2013
A233460
Prime(n), where n is such that (sum_{i=1..n} prime(i)^16) / n is an integer.
Original entry on oeis.org
2, 28751, 62639, 4620757, 6478193, 2298168044423, 128195718927553
Offset: 1
a(1) = 2, because 2 is the 1st prime and the sum of the first 1 primes^16 = 65536 when divided by 1 equals 65536 which is an integer.
Cf.
A085450 (smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n).
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t = {}; sm = 0; Do[sm = sm + Prime[n]^16; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *)
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is(n)=if(!isprime(n),return(0)); my(t=primepi(n),s); forprime(p=2,n,s+=Mod(p,t)^16); s==0 \\ Charles R Greathouse IV, Nov 30 2013
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S=n=0;forprime(p=1,,(S+=p^16)%n++||print1(p",")) \\ M. F. Hasler, Dec 01 2013
A233555
Prime(m), where m is such that (Sum_{i=1..m} prime(i)^17) / m is an integer.
Original entry on oeis.org
2, 5724469, 10534369, 16784723, 33330911, 189781037, 8418091991, 58605633953, 109388266843, 448366797199, 1056238372873, 24603683667221, 86982253895059, 100316149840769, 164029709175817, 542295448805641, 685217940914237, 1701962315686097, 23064173255594491
Offset: 1
a(1) = 2, because 2 is the 1st prime and the sum of the first 1 primes^17 = 131072 when divided by 1 equals 131072 which is an integer.
Cf.
A085450 (smallest m > 1 that divide Sum_{k=1..m} prime(k)^n).
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t = {}; sm = 0; Do[sm = sm + Prime[n]^17; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *)
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is(n)=if(!isprime(n),return(0)); my(t=primepi(n),s); forprime(p=2,n,s+=Mod(p,t)^17); s==0 \\ Charles R Greathouse IV, Nov 30 2013
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S=n=0;forprime(p=1,,(S+=p^17)%n++||print1(p",")) \\ M. F. Hasler, Dec 01 2013
A233575
Prime(m), where m is such that (Sum_{i=1..m} prime(i)^18) / m is an integer.
Original entry on oeis.org
2, 157, 1697, 190573, 167719729, 22092660553, 57613776809, 4386989244577, 91982826261331, 13432259712845291
Offset: 1
a(2) = 157, because 157 is the 37th prime and the sum of the first 37 primes^18 = 7222759943091280921446062146835136523956 when divided by 37 equals 195209728191656241120163841806355041188 which is an integer.
Cf.
A085450 = smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n.
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t = {}; sm = 0; Do[sm = sm + Prime[n]^18; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *)
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is(n)=if(!isprime(n),return(0)); my(t=primepi(n),s); forprime(p=2,n,s+=Mod(p,t)^18); s==0 \\ Charles R Greathouse IV, Nov 30 2013
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S=n=0;forprime(p=1,,(S+=p^18)%n++||print1(p",")) \\ - M. F. Hasler, Dec 01 2013
A233767
Prime(n), where n is such that (Sum_{i=1..n} prime(i)^19) / n is an integer.
Original entry on oeis.org
2, 97, 3203, 5059, 6469, 8081, 35051, 39719, 42209, 109049, 154591, 523297, 6621827, 20059771, 258196441, 731584957, 1427109029, 1899496631, 8428550519, 50790885203, 7475902096387, 22626378502139, 38855796912367, 162082298018497, 589085299527401, 4271778258271487
Offset: 1
97 is a term, because 97 is the 25th prime and the sum of the first 25 primes^19 = 71486619210134792705255313675343157050 when divided by 25 equals 2859464768405391708210212547013726282 which is an integer.
Cf.
A085450 (smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n).
-
t = {}; sm = 0; Do[sm = sm + Prime[n]^19; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *)
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is(n)=if(!isprime(n),return(0)); my(t=primepi(n),s); forprime(p=2,n,s+=Mod(p,t)^19); s==0 \\ Charles R Greathouse IV, Nov 30 2013
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my(S=n=0);forprime(p=1,,(S+=p^19)%n++||print1(p", ")) \\ M. F. Hasler, Dec 01 2013
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