_Farideh Firoozbakht (mymontain(AT)yahoo.com), _, Sep 01 2003

Edited by _Ray Chandler (rayjchandler(AT)sbcglobal.net), _, Mar 08 2010

Ray Chandler, <a href="/A087202/b087202.txt">Table of n, a(n) for n=1..1200</a>

nonn,new

nonn

a(n) is the second m (first m is A037153(n)) such that m > 1 and n!+ m is prime. For 1 < n < 630,a(n) is prime,I guess for n > 1,a(n) (compare the conjecture about A037153) is prime.

Conjecture: For n > 1, a(n) is prime (compare the conjecture about A037153).

Conjecture holds through 1200 terms.

Ray Chandler, <a href="b087202.txt">Table of n, a(n) for n=1..1200</a>

A037153[n_] := (For[m=Prime[PrimePi[n]+1], !PrimeQ[n!+m], m++ ]; m); a[n_] := (For[m=A037153[n]+1, !PrimeQ[n!+m], m++ ]; m)

easy,nonn,new

nonn

Farideh Firoozbakht (f.firoozbakhtmymontain(AT)math.ui.acyahoo.ircom), Sep 01 2003

Edited by Ray Chandler (rayjchandler(AT)sbcglobal.net), Mar 08 2010

A037153[n_] := (For[m=Prime[PrimePi[n]+1], !PrimeQ[n!+m], m++ ]; m); a[n_] := (For[m=A037153[n]+1, !PrimeQ[n!+m], m++ ]; m)

A037153[n_] := (For[m=Prime[PrimePi[n]+1], !PrimeQ[n!+m], m++ ]; m); a[n_] := (For[m=A037153[n]+1, !PrimeQ[n!+m], m++ ]; m); Table[a[n], {n, 60}]

easy,nonn,new

A037153[n_] := (For[m=Prime[PrimePi[n]+1],!PrimeQ[n!+m],m++ ]; m); a[n_] := (For[m=A037153[n]+1,!PrimeQ[n!+m],m++ ]; m)

A037153[n_] := (For[m=Prime[PrimePi[n]+1], !PrimeQ[n!+m], m++ ]; m); a[n_] := (For[m=A037153[n]+1, !PrimeQ[n!+m], m++ ]; m); Table[a[n], {n, 60}]

easy,nonn,new

A037153[n_]:=(For[m=Prime[PrimePi[n]+1],!PrimeQ[n!+m],m++ ]; m); a[n_]:=(For[m=A037153[n]+1,!PrimeQ[n!+m],m++ ]; m)

A037153[n_]:=(For[m=Prime[PrimePi[n]+1], !PrimeQ[n!+m], m++ ]; m); a[n_]:=(For[m=A037153[n]+1, !PrimeQ[n!+m], m++ ]; m); Table[a[n], {n, 60}]

easy,nonn,new

a(n) is the smallest m such that m > A037153(n) and n!+ m is prime.

4, 5, 7, 7, 11, 13, 19, 31, 23, 19, 19, 43, 73, 41, 149, 41, 53, 61, 109, 37, 37, 71, 109, 193, 97, 173, 59, 101, 229, 163, 241, 83, 139, 103, 83, 577, 397, 47, 269, 61, 211, 107, 97, 89, 379, 149, 269, 83, 137, 167, 281, 89, 79, 443, 229, 157, 179, 563, 389, 277

1,1

a(n) is the second m (first m is A037153(n)) such that m > 1 and n!+ m is prime. For 1 < n < 630,a(n) is prime,I guess for n > 1,a(n) (compare the conjecture about A037153) is prime.

A037153[n_]:=(For[m=Prime[PrimePi[n]+1],!PrimeQ[n!+m],m++ ];m); a[n_]:=(For[m=A037153[n]+1,!PrimeQ[n!+m],m++ ];m)

A037153[n_]:=(For[m=Prime[PrimePi[n]+1], !PrimeQ[n!+m], m++ ]; m); a[n_]:=(For[m=A037153[n]+1, !PrimeQ[n!+m], m++ ]; m); Table[a[n], {n, 60}]

Cf. A037153, A005235, A087200.

easy,nonn,new

Farideh Firoozbakht (f.firoozbakht(AT)math.ui.ac.ir), Sep 01 2003

approved