A186102 -id:A186102 - cp's OEIS frontend

A187882 Terms of A186102 for which A186102(n) > n + prime(n).

103, 101, 97, 197, 229, 109, 281, 233, 167, 607, 233, 349, 821, 307, 631, 1093, 853, 373, 1597, 1009, 439, 643, 503, 2111, 983, 769, 1811, 569, 2423, 3823, 3581, 2027, 941, 677, 997, 691, 1753, 3539, 1193, 5381, 4289, 2411, 2063, 1307, 919, 8311, 2719, 3187, 6373, 1459, 3331, 9431

Offset: 1

Juri-Stepan Gerasimov, Mar 14 2011

nonn

Equivalently, A186102(n) for those n where neither n nor n+prime(n) is prime.

			A186102(8) = 103 > 8 + prime(8)= 27, so a(1) = 103.

Cf. A014688, A186102.

A186102 := proc(n) local p ,pn; p := 2 ; pn := ithprime(n) ; while modp(p,pn) <> modp(n,pn) do p := nextprime(p) end do: return p ; end proc:
for n from 1 to 100 do if A186102(n) > n+ithprime(n) then printf("%d,",A186102(n)); end if; end do; # R. J. Mathar, Mar 19 2011

Definition corrected by Franklin T. Adams-Watters, Mar 16 2011

A260416 The smallest prime that is greater than prime(n) and congruent to n mod prime(n).

Original entry on oeis.org

3, 5, 13, 11, 71, 19, 41, 103, 101, 97, 73, 197, 587, 229, 109, 281, 607, 79, 421, 233, 167, 101, 521, 113, 607, 127, 233, 349, 683, 821, 1301, 163, 307, 173, 631, 1093, 1607, 853, 373, 1597, 757, 223, 1571, 1009, 439, 643, 2579, 271, 503, 2111, 983, 769, 1499, 1811, 569, 2423, 3823, 3581, 613, 2027, 1193, 941, 677, 997

Offset: 1

Ivan N. Ianakiev, Jul 25 2015

nonn

			Prime(4)=7, and the smallest prime that is greater than 7 and congruent to 4 mod 7 is 11, so a(4)=11.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A000040, A186102.

a260416 n = a260416_list !! (n-1)
a260416_list = f 1 a000040_list where
   f x (p:ps) = g ps where
       g (q:qs) = if (q - x) `mod` p == 0 then q : f (x + 1) ps else g qs
-- Reinhard Zumkeller, Aug 20 2015

lst={};Do[w=1;Label[begin];
If[PrimeQ[w*Prime[n]+n],AppendTo[lst,w*Prime[n]+n],w=w+1;Goto[begin]],{n,100}];lst

first(m)={my(v=vector(m),t,p);for(i=1,m,t=i;while(1,p=prime(t);if((p-i)%prime(i)==0,v[i]=p;break,t++);));v;} /* Anders Hellström, Aug 11 2015 */

A261192 a(0) = 2; for n>0, a(n) = smallest prime p such that p > a(n-1) and p is congruent to n modulo prime(n).

Original entry on oeis.org

2, 3, 5, 13, 53, 71, 97, 109, 179, 193, 271, 383, 419, 587, 659, 673, 811, 1433, 1543, 1627, 2221, 2357, 4051, 4339, 4919, 5651, 5783, 6619, 6983, 7877, 8053, 11969, 12739, 12911, 14629, 15233, 15287, 15737, 18131, 18743, 20627, 21163, 21943, 22963, 23011, 23291, 25717, 26633, 27031, 27743

Offset: 0

Ivan N. Ianakiev and Robert G. Wilson v, Aug 11 2015

nonn

a(n) == A186102(n) == A260416(n) (mod n).

a(10314) = 10000363333.

			a(4) = 53 because prime(4) = 7, 53 == 4 (mod 7) and 53 is the smallest such prime greater than a(3) = 13.

Ivan N. Ianakiev and Robert G. Wilson v, Table of n, a(n) for n = 0..100000

Cf. A186102, A260416.

f[n_] := f[n] = Block[{k = Prime@ n, q = Prime@ n}, While[k + n <= f[n - 1] || ! PrimeQ[k + n], k += q]; k + n]; f[0] = 2; Array[f, 50, 0]

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A187882 Terms of A186102 for which A186102(n) > n + prime(n).

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A260416 The smallest prime that is greater than prime(n) and congruent to n mod prime(n).

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A261192 a(0) = 2; for n>0, a(n) = smallest prime p such that p > a(n-1) and p is congruent to n modulo prime(n).

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